scholarly journals Duality, convexity and peak interpolation in the Drury–Arveson space

2016 ◽  
Vol 295 ◽  
pp. 90-149 ◽  
Author(s):  
Raphaël Clouâtre ◽  
Kenneth R. Davidson
Keyword(s):  
Peak Interpolation ◽  
Arveson Space

scholarly journals On a class of shift-invariant subspaces of the Drury-Arveson space

2018 ◽  
Vol 5 (1) ◽  
pp. 1-8
Author(s):  
Nicola Arcozzi ◽  
Matteo Levi
Keyword(s):  
Invariant Subspace ◽  
Invariant Subspaces ◽  
Hankel Operators ◽  
Taylor Coefficients ◽  
The Right ◽  
Arveson Space

Abstract In the Drury-Arveson space, we consider the subspace of functions whose Taylor coefficients are supported in a set Y⊂ ℕd with the property that ℕ\X + ej ⊂ ℕ\X for all j = 1, . . . , d. This is an easy example of shift-invariant subspace, which can be considered as a RKHS in is own right, with a kernel that can be explicitly calculated for specific choices of X. Every such a space can be seen as an intersection of kernels of Hankel operators with explicit symbols. Finally, this is the right space on which Drury’s inequality can be optimally adapted to a sub-family of the commuting and contractive operators originally considered by Drury.

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 Commutators and localization on the Drury–Arveson space

2011 ◽  
Vol 260 (3) ◽  
pp. 639-673 ◽  
Author(s):  
Quanlei Fang ◽  
Jingbo Xia
Keyword(s):  
Arveson Space

A peak interpolation formula for Fourier map interpretation

1986 ◽  
Vol 42 (4) ◽  
pp. 286-287 ◽  
Author(s):  
F. Pavelčík
Keyword(s):  
Interpolation Formula ◽  
Parabolic Interpolation ◽  
Computer Interpretation ◽  
Map Interpretation ◽  
Peak Interpolation

A weighted 19-point parabolic interpolation formula applicable to computer interpretation of Fourier maps is derived.

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