Equivalent Norms in Hilbert Spaces with Unconditional Bases of Reproducing Kernels

2020 ◽  
Vol 250 (2) ◽  
pp. 310-321
Author(s):  
K. P. Isaev ◽  
K. V. Trunov ◽  
R. S. Yulmukhametov
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernels ◽  
Equivalent Norms ◽  
Unconditional Bases

scholarly journals Geometry of radial Hilbert spaces with unconditional bases of reproducing kernels

2020 ◽  
Vol 12 (4) ◽  
pp. 55-63
Author(s):  
Konstantin Petrovich Isaev ◽  
Rinad Salavatovich Yulmukhametov
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernels ◽  
Unconditional Bases

scholarly journals Unconditional bases of reproducing kernels in Hilbert spaces of entire functions

2013 ◽  
Vol 5 (3) ◽  
pp. 67-76 ◽  
Author(s):  
Konstantin Petrovich Isaev ◽  
Rinad Salavatovich Yulmukhametov
Keyword(s):  
Hilbert Spaces ◽  
Entire Functions ◽  
Reproducing Kernels ◽  
Unconditional Bases

scholarly journals On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces

2017 ◽  
Vol 69 (1) ◽  
pp. 54-106 ◽  
Author(s):  
Michael Hartz
Keyword(s):  
Hilbert Spaces ◽  
Special Class ◽  
Reproducing Kernel ◽  
Reproducing Kernels ◽  
Isomorphism Problem ◽  
Reproducing Kernel Hilbert Spaces ◽  
Universal Space ◽  
Kernel Hilbert Spaces ◽  
Arveson Space ◽  
Multiplier Algebras

AbstractWe continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick property. In contrast to previous work in this area, we do not study these spaces by identifying them with the restrictions of a universal space, namely theDrury-Arveson space. Instead, we work directly with theHilbert spaces and their reproducing kernels. In particular, we show that two multiplier algebras of Nevanlinna-Pick spaces on the same set are equal if and only if the Hilbert spaces are equal. Most of the article is devoted to the study of a special class of complete Nevanlinna-Pick spaces on homogeneous varieties. We provide a complete answer to the question of when two multiplier algebras of spaces of this type are algebraically or isometrically isomorphic.This generalizes results of Davidson, Ramsey,Shalit, and the author.

scholarly journals ON THE INCLUSION RELATION OF REPRODUCING KERNEL HILBERT SPACES

2013 ◽  
Vol 11 (02) ◽  
pp. 1350014 ◽  
Author(s):  
HAIZHANG ZHANG ◽  
LIANG ZHAO
Keyword(s):  
Applied Sciences ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Reproducing Kernels ◽  
Reproducing Kernel Hilbert Spaces ◽  
Inclusion Relation ◽  
Feature Maps ◽  
Translation Invariant ◽  
Inclusion Relations ◽  
Kernel Hilbert Spaces

To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established. A full table of inclusion relations among widely-used translation invariant kernels is given. Concrete examples for Hilbert–Schmidt kernels are presented as well. We also discuss the preservation of such a relation under various operations of reproducing kernels. Finally, we briefly discuss the special inclusion with a norm equivalence.

scholarly journals General construction of reproducing kernels on a quaternionic Hilbert space

2017 ◽  
Vol 29 (05) ◽  
pp. 1750017
Author(s):  
K. Thirulogasanthar ◽  
S. Twareque Ali
Keyword(s):  
Hilbert Space ◽  
Positive Operator ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Extension Theorem ◽  
Reproducing Kernels ◽  
Reproducing Kernel Hilbert Spaces ◽  
Positive Operator Valued Measures ◽  
Kernel Hilbert Spaces ◽  
Quaternionic Hilbert Space

A general theory of reproducing kernels and reproducing kernel Hilbert spaces on a right quaternionic Hilbert space is presented. Positive operator-valued measures and their connection to a class of generalized quaternionic coherent states are examined. A Naimark type extension theorem associated with the positive operator-valued measures is proved in a right quaternionic Hilbert space. As illustrative examples, real, complex and quaternionic reproducing kernels and reproducing kernel Hilbert spaces arising from Hermite and Laguerre polynomials are presented. In particular, in the Laguerre case, the Naimark type extension theorem on the associated quaternionic Hilbert space is indicated.

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