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The tangential k-Cauchy-Fueter type operator and Penrose type integral formula on the generalized complex Heisenberg group
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作者 REN Guang-zhen SHI Yun KANG Qian-qian 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第1期181-190,共10页
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
关键词 the generalized complex Heisenberg group the tangential k-Cauchy-Fueter type operator Penrose-type integral formula
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Feynman Path Integral Using Operator Integration in Banach Space
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作者 Reza R. Ahangar Erbil Cetin Serife Muge Ege 《Journal of Applied Mathematics and Physics》 2024年第2期432-444,共13页
Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits... Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach. 展开更多
关键词 Feynman Path integral Lebesgue-Bochner-Stieltjes integral operator integral Particle-Wave Function operator integration Position and Momentum operators
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SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES F(p,q,s)
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作者 陈家乐 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期173-188,共16页
We study the closed range property and the strict singularity of integration operators acting on the spaces F(p,pα-2,s).We completely characterize the closed range property of the Volterra companion operator I_(g)on ... We study the closed range property and the strict singularity of integration operators acting on the spaces F(p,pα-2,s).We completely characterize the closed range property of the Volterra companion operator I_(g)on F(p,pα-2,s),which generalizes the existing results and answers a question raised in[A.Anderson,Integral Equations Operator Theory,69(2011),no.1,87-99].For the Volterra operator J_(g),we show that,for 0<α≤1,J_(g)never has a closed range on F(p,pα-2,s).We then prove that the notions of compactness,weak compactness and strict singularity coincide in the case of J_(g)acting on F(p,p-2,s). 展开更多
关键词 integration operator closed range property strict singularity
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q–differ-integral operator on p–valent functions associated with operator on Hilbert space
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作者 Shahram Najafzadeh 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第3期458-466,共9页
Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator i... Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated. 展开更多
关键词 multivalent function fractional q–derivative operator fractional q–integral operator Hilbert space coefficient estimate distortion bound extreme point convolution(or Hadamard product)
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Wigner function of optical cumulant operator and its dissipation in thermo-entangled state representation
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作者 张科 李兰兰 范洪义 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第6期205-210,共6页
To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive t... To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion. 展开更多
关键词 Wigner function optical cumulant operator dissipation evolution thermo-entangled state representation integration within ordered product of operators
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New light fields based on integration theory within the Weyl ordering product of operators
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作者 张科 李兰兰 +1 位作者 郭大伟 范洪义 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第4期160-164,共5页
The development of quantum optics theory based on the method of integration within an ordered product of operators(IWOP)has greatly stimulated the study of quantum states in the light field,especially non-Gaussian sta... The development of quantum optics theory based on the method of integration within an ordered product of operators(IWOP)has greatly stimulated the study of quantum states in the light field,especially non-Gaussian states with various non-classical properties.In this paper,the two-mode squeezing operator is derived with integral theory within the Weyl ordering product of operators using a combinatorial field in which one mode is a chaotic field and the other mode is a vacuum field.The density operator of the new light field,its entanglement property and photon number distribution are analyzed.We also note that tracing a three-mode pure state can yield this new light field.These methods represent a theoretical approach to investigating new density operators of light fields. 展开更多
关键词 integration within an ordered product of operators two-mode squeezing operator Weyl ordering entanglement property
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INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS 被引量:14
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作者 刘岚喆 《Acta Mathematica Scientia》 SCIE CSCD 2005年第1期89-94,共6页
It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to ... It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w). 展开更多
关键词 Nondivergence elliptic equation generalized Morrey space commutator of singular integral operator Ap weight
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Boundary properties for several singular integral operators in real Clifford analysis 被引量:7
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作者 YANG He-ju XIE Yong-hong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第3期349-358,共10页
On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Holder continuous property of some singular integral operat... On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Holder continuous property of some singular integral operators with one integral variable. Then we divide a singular integral operator with two variables into three parts and prove its Holder continuous property on the boundary. 展开更多
关键词 Singular integral operator Holder continuous function boundary property.
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Boundedness of fractional integral operators on α-modulation spaces 被引量:3
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作者 WU Xiao-mei CHEN Jie-cheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第3期339-351,共13页
In this paper, we obtain the boundedness of the fractional integral operators, the bilineax fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.
关键词 α-modulation space fractional integral operator bilinear fractional integral operator bilinearHilbert transform.
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A SHARP FUNCTION ESTIMATE FOR MULTILINEAR SINGULAR INTEGRAL OPERATORS 被引量:5
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作者 Hu Guoen(Department of Applied Mathematics Institute of Information Engineering P. O. Box 1001-747, Zhengzhou 450002 PRC) 《Analysis in Theory and Applications》 2000年第1期17-25,共9页
A variant sharp function estimate is established for the multilinear singular integral operators. Two applications of this estimate are also given.
关键词 oscillatory integral operator MULTIPLIER SINGULARITY
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Compactness for the commutators of multilinear singular integral operators with non-smooth kernels 被引量:2
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作者 BU Rui CHEN Jie-cheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2019年第1期55-75,共21页
In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered. By some new maximal functions... In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered. By some new maximal functions to control the commutators of bilinear singular integral operators and CMO(Rn) functions, compactness for the commutators is proved. 展开更多
关键词 singular integral operator maximal function weighted norm inequality COMMUTATOR compact operator
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The Boundedness of Singular Integral Operator along an Open Curve 被引量:3
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作者 Wang Xiaolin Min Honglin(College of Mathematical Sciences, Wuhan University, Wuhan 430072, China) 《Wuhan University Journal of Natural Sciences》 CAS 1998年第4期383-388,共6页
It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS... It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH * intoH *. In this paper, we define a Banach space , and prove that is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators. 展开更多
关键词 singular integral operator SPACE BOUNDEDNESS
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ON THE BOUNDEDNESS AND THE NORM OF A CLASS OF INTEGRAL OPERATORS 被引量:2
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作者 周立芳 《Acta Mathematica Scientia》 SCIE CSCD 2015年第6期1475-1482,共8页
The boundedness and the norm of a class of integral operators Ta,b,c on Lλ^P spaces are studied in this paper. The author not only gives the sufficient and necessary condition for the boundedness of Ta,b,c on Lλ^P,b... The boundedness and the norm of a class of integral operators Ta,b,c on Lλ^P spaces are studied in this paper. The author not only gives the sufficient and necessary condition for the boundedness of Ta,b,c on Lλ^P,but also obtains its accurate norm on Lλ^P for some range under the condition of c = n + a + b. 展开更多
关键词 integral operators sufficient condition necessary condition operator norm hypergeometric functions
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ENDPOINT ESTIMATES FOR FRACTIONAL INTEGRAL ASSOCIATED TO SCHRDINGER OPERATORS ON THE HEISENBERG GROUPS 被引量:2
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作者 江寅生 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期993-1000,共8页
Let ∠= -△Hn+ V be the Schrdinger operator on the Heisenberg groups Hn,where V is a nonnegative function satisfying the reverse Hlder inequality. In this article, the author obtains the BMO_∠ and BLO_∠ estimates o... Let ∠= -△Hn+ V be the Schrdinger operator on the Heisenberg groups Hn,where V is a nonnegative function satisfying the reverse Hlder inequality. In this article, the author obtains the BMO_∠ and BLO_∠ estimates of the fractional integrals associated to ∠. 展开更多
关键词 Schrdinger operator Heisenberg group BMO_∠ BLO_∠ fractional integral
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The Fractional Maximal Operator and Marcinkiewicz Integrals Associated with Schr?dinger Operators on Morrey Spaces with Variable Exponent 被引量:2
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作者 Yu Shu Min Wang 《Analysis in Theory and Applications》 CSCD 2015年第1期68-80,共13页
In this paper, we prove the boundedness of the fractional maximal operator, Hardy-Littlewood maximal operator and marcinkiewicz integrals associated with Schrodinger operator on Morrey spaces with variable exponent.
关键词 Fractional maximal operator Marcinkiewicz integrals SCHRODINGER variable exponent Morrey space
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QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS 被引量:1
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作者 Wenhua GAO Guoen HU 《Acta Mathematica Scientia》 SCIE CSCD 2019年第4期1149-1162,共14页
In this article, the authors consider the weighted bounds for the singular integral operator defined by ■where ? is homogeneous of degree zero and has vanishing moment of order one, and A is a function on Rnsuch that... In this article, the authors consider the weighted bounds for the singular integral operator defined by ■where ? is homogeneous of degree zero and has vanishing moment of order one, and A is a function on Rnsuch that ?A ∈ BMO(R^n). By sparse domination, the authors obtain some quantitative weighted bounds for TAwhen ? satisfies regularity condition of Lr-Dini type for some r ∈(1, ∞). 展开更多
关键词 SINGULAR integral operator sparse DOMINATION Ap constant MAXIMAL operA TOR
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Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces 被引量:1
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作者 Yuexiang He Yueshan Wang 《Analysis in Theory and Applications》 CSCD 2016年第1期90-102,共13页
Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I (the identity operator). Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this pa... Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I (the identity operator). Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively. 展开更多
关键词 Toeplitz type operator singular integral operator variable calderon-zygmund kernel weighted BMO function weighted Lipschitz function weighted Morrey space.
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ON THE COMMUTATORS OF SINGULAR INTEGRAL OPERATORS 被引量:1
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作者 胡国恩 《Acta Mathematica Scientia》 SCIE CSCD 2005年第3期545-554,共10页
Lp(Rn) (1<p<∞) boundedness and a weak type endpoint estimate are considered for the commutators of singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness o... Lp(Rn) (1<p<∞) boundedness and a weak type endpoint estimate are considered for the commutators of singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness of the singular integral operators implies the LP(Rn) boundedness (1<p<∞) and the weak type (H1(Rn), L1(Rn)) boundedness for the corresponding commutators. A new interpolation theorem is also established. 展开更多
关键词 COMMUTATOR singular integral operators BMO(R^N) INTERPOLATION
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BOUNDEDNESS OF HIGHER ORDER COMMUTATORS OF GENERALIZED FRACTIONAL INTEGRAL OPERATORS ON HARDY SPACES 被引量:2
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作者 Chunlei He Lisheng Shu 《Analysis in Theory and Applications》 2005年第3期249-257,共9页
Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-t... Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces. 展开更多
关键词 (θ - N)-type fractional integral operator COMMUTATOR BMO space Hardy space Herz-type Hardy space ATOM
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Weighted Boundedness for Generalized Maximal andSingular Integral Operators in Orlicz-Morrey Spaces 被引量:2
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作者 刘岚喆 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第2期51-57, ,共7页
In this paper,the weighted boundedness for the generalised maximal and singular integral operator in Orlicz-Morrey spaces are obtained.
关键词 homogeneous type space maximal operator singular integral operator Orlicz-Morrey space
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