The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.I...The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.展开更多
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously r...In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.展开更多
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends ...In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.展开更多
In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis...In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.展开更多
Let A ∈ B(X) and B ∈ B(Y), Me be an operator on Banach space X + Y given by Mc =(A C 0 B)A generalized Drazin spectrum defined by σgD(T) = {λ∈C : T-λI is not generalized Drazin invertible} is considere...Let A ∈ B(X) and B ∈ B(Y), Me be an operator on Banach space X + Y given by Mc =(A C 0 B)A generalized Drazin spectrum defined by σgD(T) = {λ∈C : T-λI is not generalized Drazin invertible} is considered in this paper. It is shown that展开更多
In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G (i.e., nilpotent stratified Lie group) in the generalized Morrey spaces Mp,φ(G), where Q is the homogeneous dimens...In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G (i.e., nilpotent stratified Lie group) in the generalized Morrey spaces Mp,φ(G), where Q is the homogeneous dimension of G. We find the conditions on the pair (φ1, φ2) which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 (G) to another Mq,φ2 (G), 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 (G) to the weak space Wq,φ2 (G), 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α (G) from Mp,φ^1/p(G)to Mq,φ^1/q(G) for 1 〈p〈q〈∞ and fromM1,φ(G) toWMq,φ^1/q(G)for 1〈q〈∞. In the case b ∈ BMO(G) and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair (φ1, φ2) which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 (G) to Mq,φ2(G) with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p(G) tom Mp,φ^1/p (G) for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on (φ1, φ2) and φ , which do not assume any assumption on monotonicity of (φ1, φ2) and φ in r. As applications we consider the SchrSdinger operator -△G + V on G, where the nonnegative potential V belongs to the reverse Holder class B∞(G). The MB,φ1 - Mq,φ2 estimates for the operators V^γ(-△G + V)^-β and V^γ△↓G(-△G + V)^-β are obtained.展开更多
In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma"...In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in [12] where "the generalized Banach lemma" was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.展开更多
The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.
Let A be a subalgebra of B(X) containing the identity operator I and an idempotent P. Suppose that α,β: A →A are ring epimorphisms and there exists some nest N on 2( such that α(P)(X) and β(P)(X) are ...Let A be a subalgebra of B(X) containing the identity operator I and an idempotent P. Suppose that α,β: A →A are ring epimorphisms and there exists some nest N on 2( such that α(P)(X) and β(P)(X) are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ : A→ B(X) be an additive mapping. It is shown that, if δ is (α, β)-derivable at zero point, then there exists an additive (α, β)-derivation τ : A →β(X) such that δ(A) =τ(A) + α(A)δ(I) for all A∈A. It is also shown that if δ is generalized (α,β)-derivable at zero point, then δ is an additive generalized (α, β)-derivation. Moreover, by use of this result, the additive maps (generalized) (α,β)-derivable at zero point on several nest algebras, are also characterized.展开更多
By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral (dyduexp [iu(q-Q)+iy(p-P)+is/2yu]) from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization...By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral (dyduexp [iu(q-Q)+iy(p-P)+is/2yu]) from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.展开更多
In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson ...In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson condition,bounded Toeplitz operators,compact Toeplitz operators,and Toeplitz operators in the Schatten-p class are all considered.展开更多
Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO(G) functions on Herz spaces in the setting of homogeneous group. This article ex...Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO(G) functions on Herz spaces in the setting of homogeneous group. This article extends some known results.展开更多
Compared with the Hamiltonian mechanics and the Lagrangian mechanics,the Birkhoffian mechanics is more general.The Birkhoffian mechanics is discussed on the basis of the generalized fractional operators,which are prop...Compared with the Hamiltonian mechanics and the Lagrangian mechanics,the Birkhoffian mechanics is more general.The Birkhoffian mechanics is discussed on the basis of the generalized fractional operators,which are proposed recently.Therefore,differential equations of motion within generalized fractional operators are established.Then,in order to find the solutions to the differential equations,Noether symmetry,conserved quantity,perturbation to Noether symmetry and adiabatic invariant are investigated.In the end,two applications are given to illustrate the methods and results.展开更多
In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation o...In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation of renormalization procedure is given under white noise theory.展开更多
In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spa...In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spaces.展开更多
We obtain weak type (1, q) inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the str...We obtain weak type (1, q) inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the strong type inequalities in [13, 14, 15].展开更多
Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almo...Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in ερ,φ.展开更多
In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not pre...In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.展开更多
In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green fun...In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.展开更多
Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok (p, q) with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respec...Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok (p, q) with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 (p - P) (q - Q), (q - Q) 3 (p - P), and (p, q), which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of (p, q) are also derived, which helps us to put the operators into their - and - ordering, respectively.展开更多
基金Supported by National Nature Science Foundation in China(12101564,11971425,11801508)Nature Science Foundation of Zhejiang province(LY22A010013)Domestic Visiting Scholar Teacher Professional Development Project(FX2021042)。
文摘The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.
文摘In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.
文摘In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.
文摘In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.
基金Supported by the National Natural Science Foundation of China(11301077,1117131,11171066 and11226113)Foundation of the Education Department of Fujian Province(JA12074)the Natural ScienceFoundation of Fujian Province(2012J05003)
文摘Let A ∈ B(X) and B ∈ B(Y), Me be an operator on Banach space X + Y given by Mc =(A C 0 B)A generalized Drazin spectrum defined by σgD(T) = {λ∈C : T-λI is not generalized Drazin invertible} is considered in this paper. It is shown that
基金partially supported by the grant of Ahi Evran University Scientific Research Projects(FEN 4001.12.0018)partially supported by the grant of Ahi Evran University Scientific Research Projects(FEN 4001.12.0019)+1 种基金by the grant of Science Development Foundation under the President of the Republic of Azerbaijan project EIF-2010-1(1)-40/06-1partially supported by the Scientific and Technological Research Council of Turkey(TUBITAK Project No:110T695)
文摘In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G (i.e., nilpotent stratified Lie group) in the generalized Morrey spaces Mp,φ(G), where Q is the homogeneous dimension of G. We find the conditions on the pair (φ1, φ2) which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 (G) to another Mq,φ2 (G), 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 (G) to the weak space Wq,φ2 (G), 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α (G) from Mp,φ^1/p(G)to Mq,φ^1/q(G) for 1 〈p〈q〈∞ and fromM1,φ(G) toWMq,φ^1/q(G)for 1〈q〈∞. In the case b ∈ BMO(G) and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair (φ1, φ2) which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 (G) to Mq,φ2(G) with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p(G) tom Mp,φ^1/p (G) for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on (φ1, φ2) and φ , which do not assume any assumption on monotonicity of (φ1, φ2) and φ in r. As applications we consider the SchrSdinger operator -△G + V on G, where the nonnegative potential V belongs to the reverse Holder class B∞(G). The MB,φ1 - Mq,φ2 estimates for the operators V^γ(-△G + V)^-β and V^γ△↓G(-△G + V)^-β are obtained.
基金Supported by the Nature Science Foundation of China(11471091 and 11401143)
文摘In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in [12] where "the generalized Banach lemma" was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.
文摘The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.
文摘Let A be a subalgebra of B(X) containing the identity operator I and an idempotent P. Suppose that α,β: A →A are ring epimorphisms and there exists some nest N on 2( such that α(P)(X) and β(P)(X) are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ : A→ B(X) be an additive mapping. It is shown that, if δ is (α, β)-derivable at zero point, then there exists an additive (α, β)-derivation τ : A →β(X) such that δ(A) =τ(A) + α(A)δ(I) for all A∈A. It is also shown that if δ is generalized (α,β)-derivable at zero point, then δ is an additive generalized (α, β)-derivation. Moreover, by use of this result, the additive maps (generalized) (α,β)-derivable at zero point on several nest algebras, are also characterized.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11147009)the Natural Science Foundation of Shandong Province of China (Grant No. ZR2010AQ027)the Program of Higher Educational Science and Technology of Shandong Province,China (Grant No. J10LA15)
文摘By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral (dyduexp [iu(q-Q)+iy(p-P)+is/2yu]) from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.
基金Supported by National Natural Science Foundation of China(11471084,11301101,11971125)Young Innovative Talent Project of Department of Edcucation of Guangdong Province(2017KQNCX220)the Natural Research Project of Zhaoqing University(221622).
文摘In this article,we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces Fψ^2.Main results including Fock-Carleson condition,bounded Toeplitz operators,compact Toeplitz operators,and Toeplitz operators in the Schatten-p class are all considered.
基金Supported by Chinese Universities Scientific Fund(2009RC0703 of BUPT)the NNSF of China (10871024)
文摘Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO(G) functions on Herz spaces in the setting of homogeneous group. This article extends some known results.
基金This work was supported by the National Natural Science Foun-dation of China(Grants 11802193 and 11972241)the Natural Sci-ence Foundation of Jiangsu Province(Grant BK20191454)the Young Scientific and Technological Talents Promotion Project of Suzhou Association for Science and Technology.
文摘Compared with the Hamiltonian mechanics and the Lagrangian mechanics,the Birkhoffian mechanics is more general.The Birkhoffian mechanics is discussed on the basis of the generalized fractional operators,which are proposed recently.Therefore,differential equations of motion within generalized fractional operators are established.Then,in order to find the solutions to the differential equations,Noether symmetry,conserved quantity,perturbation to Noether symmetry and adiabatic invariant are investigated.In the end,two applications are given to illustrate the methods and results.
基金Project supported by NSFC (10171035) and Hubei University Youth Foundation (97A012)
文摘In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation of renormalization procedure is given under white noise theory.
文摘In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spaces.
基金Supported by Fundamental Research Program 2011-2012
文摘We obtain weak type (1, q) inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the strong type inequalities in [13, 14, 15].
文摘Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in ερ,φ.
文摘In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.
文摘In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.
基金Project supported by the National Natural Science Foundation of China(Grant No.11175113)the Natural Science Foundation of Shandong Province of China(Grant No.Y2008A16)+1 种基金the University Experimental Technology Foundation of Shandong Province of China(Grant No.S04W138)the Natural Science Foundation of Heze University of Shandong Province of China(Grants Nos.XY07WL01 and XY08WL03)
文摘Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok (p, q) with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 (p - P) (q - Q), (q - Q) 3 (p - P), and (p, q), which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of (p, q) are also derived, which helps us to put the operators into their - and - ordering, respectively.