Little Hankel Operators between Bergman Spaces of the Right Half Plane - NZJM

New Zealand Journal of Mathematics

N. DasP. G. Dept. of MathematicsUtkal UniversityVaniviharBhubaneswar751004, OrissaINDIA$$¹ 

关键词: Tangent space;    cone;    quadric hypersurface;    strange curve;    strange variety;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: University of Auckland * Department of Mathematics

【 摘 要 】

In this paper we consider a class of weighted integral operators on L2 (0, ) and show that they are unitarily equivalent to little Hankel operators between weighted Bergman spaces of the right half plane. We use two parametersand involve two weights to define Bergman spaces of the domain and range of the little Hankel operators. We obtained conditions for the Hankel integral operator to be Hilbert-Schmidt, nuclear, finite rank and compact, expressed in terms of the kernel of the integral operator. For certain class of weights, these operators are shown to be unitarily equivalent to little Hankel operators between weighted Bergman spaces of the disk, and the symbol correspondence is given. In view of the strong link between Hankel operators and best approximation, some asymptotic results on the singular values of Hankel integral operators are also provided.

【 授权许可】

Unknown