scholarly journals Behavior of Gabor frame operators on Wiener amalgam spaces

2016 ◽  
Vol 14 (04) ◽  
pp. 1650028 ◽  
Author(s):  
Anirudha Poria
Keyword(s):  
Weak Sense ◽  
Gabor Frame ◽  
Operator Norm ◽  
Identity Operator ◽  
Frame Operator ◽  
Wiener Amalgam Spaces ◽  
Sampling Density ◽  
Amalgam Spaces

It is well-known that the Gabor expansions converge to identity operator in weak* sense on the Wiener amalgam spaces as sampling density tends to infinity. In this paper, we prove the convergence of Gabor expansions to identity operator in the operator norm as well as weak* sense on [Formula: see text] as the sampling density tends to infinity. Also we show the validity of the Janssen’s representation and the Wexler–Raz biorthogonality condition for Gabor frame operator on [Formula: see text].

scholarly journals Hilbert space valued Gabor frames in weighted amalgam spaces

2019 ◽  
Vol 10 (4) ◽  
pp. 377-394
Author(s):  
Anirudha Poria ◽  
Jitendriya Swain
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Gabor Frame ◽  
Window Function ◽  
Gabor Frames ◽  
Frame Operator ◽  
Wiener Amalgam Space ◽  
Amalgam Spaces ◽  
Special Case

AbstractLet {\mathbb{H}} be a separable Hilbert space. In this paper, we establish a generalization of Walnut’s representation and Janssen’s representation of the {\mathbb{H}}-valued Gabor frame operator on {\mathbb{H}}-valued weighted amalgam spaces {W_{\mathbb{H}}(L^{p},L^{q}_{v})}, {1\leq p,q\leq\infty}. Also, we show that the frame operator is invertible on {W_{\mathbb{H}}(L^{p},L^{q}_{v})}, {1\leq p,q\leq\infty}, if the window function is in the Wiener amalgam space {W_{\mathbb{H}}(L^{\infty},L^{1}_{w})}. Further, we obtain the Walnut representation and invertibility of the frame operator corresponding to Gabor superframes and multi-window Gabor frames on {W_{\mathbb{H}}(L^{p},L^{q}_{v})}, {1\leq p,q\leq\infty}, as a special case by choosing the appropriate Hilbert space {\mathbb{H}}.

Continuity of Gabor Frame Operators On Weighted Wiener Amalgam Spaces

2015 ◽  
Vol 20 (1) ◽  
pp. 1-6
Author(s):  
Mr. Vishad Tiwari ◽  
◽  
Dr. J.K Maitra ◽  
Dr. Ashish Kumar
Keyword(s):  
Gabor Frame ◽  
Wiener Amalgam Spaces ◽  
Amalgam Spaces

Convergence of the inverse continuous wavelet transform in Wiener amalgam spaces

Analysis ◽  
2015 ◽  
Vol 35 (1) ◽  
Author(s):  
Ferenc Weisz
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Fourier Transforms ◽  
Weak Sense ◽  
Continuous Wavelet ◽  
Norm Convergence ◽  
Wiener Amalgam Spaces ◽  
Summability Methods ◽  
Lebesgue Points ◽  
Amalgam Spaces

AbstractThe inversion formula for the continuous wavelet transform is usually considered in the weak sense. With the help of summability methods of Fourier transforms we obtain norm convergence and convergence at Lebesgue points of the inverse wavelet transform for functions from the

scholarly journals Invertibility of the Gabor frame operator on the Wiener amalgam space

2008 ◽  
Vol 153 (2) ◽  
pp. 212-224 ◽  
Author(s):  
Ilya A. Krishtal ◽  
Kasso A. Okoudjou
Keyword(s):  
Gabor Frame ◽  
Frame Operator ◽  
Wiener Amalgam Space

scholarly journals States which have a trace-like property relative to a C*-subalgebra of B(H)

1976 ◽  
Vol 17 (2) ◽  
pp. 158-160
Author(s):  
Guyan Robertson
Keyword(s):  
Hilbert Space ◽  
Spectral Radius ◽  
Operator Theory ◽  
Linear Operators ◽  
Operator Norm ◽  
Identity Operator ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Image Position

In what follows, B(H) will denote the C*-algebra of all bounded linear operators on a Hilbert space H. Suppose we are given a C*-subalgebra A of B(H), which we shall suppose contains the identity operator 1. We are concerned with the existence of states f of B(H) which satisfy the following trace-like relation relative to A:Our first result shows the existence of states f satisfying (*), when A is the C*-algebra C*(x) generated by a normaloid operator × and the identity. This allows us to give simple proofs of some well-known results in operator theory. Recall that an operator × is normaloid if its operator norm equals its spectral radius.

p-FRAMES FOR SUBSPACES OF WIENER AMALGAMS ON A LOCALLY COMPACT ABELIAN GROUP

2003 ◽  
Vol 01 (04) ◽  
pp. 481-489
Author(s):  
S. S. PANDEY
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Closed Subspace ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Wiener Amalgam Spaces ◽  
Amalgam Spaces

We prove a theorem to characterize the p-frames for a shift invariant closed subspace of Wiener amalgam spaces [Formula: see text], 1 ≤ p ≤ q ≤ ∞, [Formula: see text] being a locally compact abelian group. Also, we show that a collection of translates under approximate conditions generaltes a p-frames for the space [Formula: see text].

scholarly journals Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Ferenc Weisz
Keyword(s):  
Fourier Series ◽  
Fourier Transforms ◽  
Lebesgue Point ◽  
Strong Summability ◽  
Wiener Amalgam Spaces ◽  
Wiener Amalgam Space ◽  
Almost Everywhere ◽  
Lebesgue Points ◽  
Amalgam Spaces

We characterize the set of functions for which strong summability holds at each Lebesgue point. More exactly, iffis in the Wiener amalgam spaceW(L1,lq)(R)andfis almost everywhere locally bounded, orf∈W(Lp,lq)(R)  (1<p<∞,1≤q<∞), then strongθ-summability holds at each Lebesgue point off. The analogous results are given for Fourier series, too.

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