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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Monatshefte für Math...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Monatshefte für Mathematik
Article . 1993 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1993
Data sources: zbMATH Open
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On Calder�n-Toeplitz operators

On Calderón-Toeplitz operators
Authors: Nowak, Krzysztof;

On Calder�n-Toeplitz operators

Abstract

Let \(\psi\in L^ 2(\mathbb{R}^ d)\) be an admissible wavelet, \(\psi_ \xi(x)= t^{-d/2} \psi\Bigl({x-v\over t}\Bigr)\), \(\xi= (v,t)\), \(G\) the ``\(ax+ b\)''-group, i.e. \(G=\{\xi= (v,t): v\in \mathbb{R}^ d, t>0\}\), \(d\xi= t^{d-1}dv dt\) the left invariant measure on \(G\). For a Borel measure \(\mu\) on \(G\), for which \[ {\mathcal D}(T_ \mu)= \left\{f\in L_ 2(\mathbb{R}^ d): \int_ G |\langle f,\psi_ \xi\rangle|^ 2 d|\mu|<\infty\right\} \] is dense in \(L^ 2(\mathbb{R}^ d)\), a Calderón-Toeplitz operator is defined by the formula \[ \langle T_ \mu f,g\rangle= \int_ G \langle f,\psi_ \xi\rangle\langle\psi_ \xi,g\rangle d\mu, \] where \(f,g\in {\mathcal D}(T_ \mu)\). Calderón-Toeplitz operators are connected with Calderón-Zygmund operators. On the other hand these operators generalize Toeplitz operators defined on weight Bergman spaces on the upper half plane. The author discusses boundness and Schatten ideal criteria for a class Calderón-Toeplitz operators.

Keywords

Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), left invariant measure, admissible wavelet, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Calderón-Zygmund operators, boundness, Schatten ideal, General harmonic expansions, frames, singular numbers, Article, Borel measure, Calderón-Toeplitz operator, 510.mathematics, Toeplitz operators, Hankel operators, Wiener-Hopf operators, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
9
Average
Average
Average
Green