调和Fock的对偶空间  

Dual spaces of harmonic Fock spaces

作　　者：黄穗 李勇强 HUANG Sui;LI Yongqiang(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院

出　　处：《厦门大学学报（自然科学版）》2024年第6期1112-1117,共6页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(118711270);重庆市科委科研项目(CSTC2019JCYJ-MSXM0295);重庆师范大学数学科学学院重点实验室开放课题(CSSXKFKTM202002)。

摘　　要：[目的]调和Fock空间对偶空间的表示促进了对函数空间上自伴算子、Toeplitz算子、对偶算子等特殊算子性质的研究.此外,对偶空间理论在诸如遥感领域、经济学领域、计算机通信领域、量子力学等领域有着非常重要的作用.本文在调和Fock空间的研究基础上,研究调和Fock空间对偶空间的具体表示.[方法]构造了调和Fock空间中全体再生核张成的线性子空间,证明其在调和Fock空间中稠密.然后借助泛函在此稠子空间上的性质,利用解析Fock空间对偶空间的讨论方法,研究调和Fock空间的对偶空间的表示.[结果]得到调和Fock空间对偶空间的两个结果:当1<p<∞时,(F_(h,α)^(p))^(*)=F_(h,β)^(q),其中1/p+1/q=1.当p=1时,(F_(h,α)^(1))=F_(h,β)^(∞).这两个结果分别对应了当1<p<∞与当p=1时,调和Fock空间对偶空间的表示.特别地,如果α=β,还能得到以下推论:当1≤p<∞时,(F_(h,α)^(p))^(*)=F_(h,α)^(q).[结论]目前已通过经典方法得到了当1≤p<∞时调和Fock空间对偶空间的表示.该结果将会在调和Fock空间的后续研究中使用.[Objective]The representation of the dual space of harmonic Fock space promotes the study of properties of special operators such as self-adjoint operators,Toeplitz operators and dual operators on function Spaces.In addition,dual space theory plays a very important role in fields such as remote sensing,economics,computer communication,and quantum mechanics among others.Based on the research of harmonic Fock space,herein we study the concrete representation of the dual space of harmonic Fock space.[Methods]In this paper,a linear subspace of all reproducing kernels in harmonic Fock space is constructed and proved to be dense in harmonic Fock space.Then,by virtue of properties of functional on this dense subspace,we study the representation of the dual space of harmonic Fock space via discussing the dual space of analytic Fock space.[Results]We obtain two results for dual spaces of harmonic Fock spaces:when 1<p<∞,(F_(h,α)^(p))^(*)=F_(h,β)^(q),where 1/p+1/q=1.When p=1,((F_(h,α)^(1))=F_(h,β)^(∞).These two results correspond to the representation of the dual space of the harmonic Fock space when 1<p<∞and p=1,respectively.In particular,ifα=β,we also develop the following corollary:when 1≤p<∞,(F_(h,α)^(p))=F_(h,α)^(q) .[Conclusion]At present,the representation of the dual space of the harmonic Fock space has been obtained by classical methods.These results will be used in subsequent studies of harmonic Fock spaces.

关 键 词：调和Fock空间 再生核 对偶空间 

分 类 号：O177[理学—数学]