The reseearch on the relation between weighted shift operators on Hilbert spaces and other important class of operators attracted the attention of some mathematicians. For example, the relation between weighted shift ...The reseearch on the relation between weighted shift operators on Hilbert spaces and other important class of operators attracted the attention of some mathematicians. For example, the relation between weighted shift operators and subnormal operators has been thoroughly studied by J. Stampfli, R. Gellar and D. A. Herrero, etc. (see reference [1]) But the decomposability of weighted shift operators has not yet attracted enough attention up to now. We made initial research展开更多
High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than l...High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones;but for fractional operators the stencils for high order schemes and low order ones are the same.Then using high order schemes to solve fractional equations leads to almost the same computational cost with first order schemes but the accuracy is greatly improved.Using the fractional linear multistep methods,Lubich obtains the n-th order(n≤6)approximations of the a-th derivative(a>0)or integral(a<0)[Lubich,SIAM J.Math.Anal.,17,704-719,1986],because of the stability issue the obtained scheme can not be directly applied to the space fractional operator with a∈(1,2)for time dependent problem.By weighting and shifting Lubich’s 2nd order discretization scheme,in[Chen&Deng,SINUM,arXiv:1304.7425]we derive a series of effective high order discretizations for space fractional derivative,called WSLD operators there.As the sequel of the previous work,we further provide new high order schemes for space fractional derivatives by weighting and shifting Lubich’s 3rd and 4th order discretizations.In particular,we prove that the obtained 4th order approximations are effective for space fractional derivatives.And the corresponding schemes are used to solve the space fractional diffusion equation with variable coefficients.展开更多
For an operator weighted shift S,the essential spectrum σ_e(S) and the indices associated with holes in σ_e(S) are described.Moreover,Banach reducibility of S is investigated and a condition for S~* to be a Cowen-Do...For an operator weighted shift S,the essential spectrum σ_e(S) and the indices associated with holes in σ_e(S) are described.Moreover,Banach reducibility of S is investigated and a condition for S~* to be a Cowen-Douglas operator is characterized.展开更多
Abstract Let H be a complex seperable Hilbert space and ^（Jt^） denote the collection of bounded linear operators on H. For an operator in L（H）, rad{A}＇ denotes the Jacobson radical of the commutant of A. This pap...Abstract Let H be a complex seperable Hilbert space and ^（Jt^） denote the collection of bounded linear operators on H. For an operator in L（H）, rad{A}＇ denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}＇/rad{A}＇. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative.展开更多
文摘The reseearch on the relation between weighted shift operators on Hilbert spaces and other important class of operators attracted the attention of some mathematicians. For example, the relation between weighted shift operators and subnormal operators has been thoroughly studied by J. Stampfli, R. Gellar and D. A. Herrero, etc. (see reference [1]) But the decomposability of weighted shift operators has not yet attracted enough attention up to now. We made initial research
基金supported by the National Natural Science Foundation of China under Grant No.11271173,the Fundamental Research Funds for the Central Universities under Grant No.lzujbky-2014-228,and the Program for New Century Excellent Talents in University under Grant No.NCET-09-0438.
文摘High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones;but for fractional operators the stencils for high order schemes and low order ones are the same.Then using high order schemes to solve fractional equations leads to almost the same computational cost with first order schemes but the accuracy is greatly improved.Using the fractional linear multistep methods,Lubich obtains the n-th order(n≤6)approximations of the a-th derivative(a>0)or integral(a<0)[Lubich,SIAM J.Math.Anal.,17,704-719,1986],because of the stability issue the obtained scheme can not be directly applied to the space fractional operator with a∈(1,2)for time dependent problem.By weighting and shifting Lubich’s 2nd order discretization scheme,in[Chen&Deng,SINUM,arXiv:1304.7425]we derive a series of effective high order discretizations for space fractional derivative,called WSLD operators there.As the sequel of the previous work,we further provide new high order schemes for space fractional derivatives by weighting and shifting Lubich’s 3rd and 4th order discretizations.In particular,we prove that the obtained 4th order approximations are effective for space fractional derivatives.And the corresponding schemes are used to solve the space fractional diffusion equation with variable coefficients.
基金Supported by MCME.Doctoral Foundation of the Ministry of Education and Science Foundation of Liaoning University
文摘For an operator weighted shift S,the essential spectrum σ_e(S) and the indices associated with holes in σ_e(S) are described.Moreover,Banach reducibility of S is investigated and a condition for S~* to be a Cowen-Douglas operator is characterized.
文摘Abstract Let H be a complex seperable Hilbert space and ^（Jt^） denote the collection of bounded linear operators on H. For an operator in L（H）, rad{A}＇ denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}＇/rad{A}＇. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative.
