scholarly journals Pre-Dual of Fofana’s Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 528 ◽  
Author(s):  
Hans G. Feichtinger ◽  
Justin Feuto
Keyword(s):  
Wiener Amalgam Spaces ◽  
Amalgam Spaces ◽  
Invariant Spaces

The purpose of this paper is to characterize the pre-dual of the spaces introduced by I. Fofana on the basis of Wiener amalgam spaces. These spaces have a specific dilation behaviour similar to the spaces L α ( R d ) . The characterization of the pre-dual will be based on the idea of minimal invariant spaces (with respect to such a group of dilation operators).

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.

scholarly journals Inclusion relations between Lp-Sobolev and Wiener amalgam spaces

2015 ◽  
Vol 268 (1) ◽  
pp. 239-254 ◽  
Author(s):  
Jayson Cunanan ◽  
Masaharu Kobayashi ◽  
Mitsuru Sugimoto
Keyword(s):  
Wiener Amalgam Spaces ◽  
Inclusion Relations ◽  
Amalgam Spaces

ON THE SCATTERING THEORY OF MASSLESS NELSON MODELS

2002 ◽  
Vol 14 (11) ◽  
pp. 1165-1280 ◽  
Author(s):  
C. GÉRARD
Keyword(s):  
Scattering Theory ◽  
Bound States ◽  
Relativistic Quantum ◽  
Asymptotic Completeness ◽  
Induced Representations ◽  
Vacuum States ◽  
Relativistic Atom ◽  
Propagation Properties ◽  
Invariant Spaces

We study the scattering theory for a class of non-relativistic quantum field theory models describing a confined non-relativistic atom interacting with a massless relativistic bosonic field. We construct invariant spaces [Formula: see text] which are defined in terms of propagation properties for large times and which consist of states containing a finite number of bosons in the region {|x| ≥ ct} for t → ±∞. We show the existence of asymptotic fields and we prove that the associated asymptotic CCR representations preserve the spaces [Formula: see text] and induce on these spaces representations of Fock type. For these induced representations, we prove the property of geometric asymptotic completeness, which gives a characterization of the vacuum states in terms of propagation properties. Finally we show that a positive commutator estimate imply the asymptotic completeness property, i.e. the fact that the vacuum states of the induced representations coincide with the bound states of the Hamiltonian.

scholarly journals Changes of variables in modulation and Wiener amalgam spaces

2011 ◽  
Vol 284 (16) ◽  
pp. 2078-2092 ◽  
Author(s):  
Michael Ruzhansky ◽  
Mitsuru Sugimoto ◽  
Joachim Toft ◽  
Naohito Tomita
Keyword(s):  
Wiener Amalgam Spaces ◽  
Amalgam Spaces

scholarly journals Hausdorff operators on modulation and Wiener amalgam spaces

2018 ◽  
Vol 9 (3) ◽  
pp. 398-412 ◽  
Author(s):  
Guoping Zhao ◽  
Dashan Fan ◽  
Weichao Guo
Keyword(s):  
Wiener Amalgam Spaces ◽  
Hausdorff Operators ◽  
Amalgam Spaces
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