Unique continuation for the Schroedinger equation with potentials in Wiener amalgam spaces

2011 ◽  
Vol 60 (4) ◽  
pp. 1203-1228 ◽  
Author(s):  
Ihyeok Seo
Keyword(s):  
Unique Continuation ◽  
Schroedinger Equation ◽  
Wiener Amalgam Spaces ◽  
Amalgam Spaces

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

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

scholarly journals Norm Inflation for Benjamin–Bona–Mahony Equation in Fourier Amalgam and Wiener Amalgam Spaces with Negative Regularity

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3145
Author(s):  
Divyang G. Bhimani ◽  
Saikatul Haque
Keyword(s):  
Initial Data ◽  
Modulation Spaces ◽  
Well Posedness ◽  
Wiener Amalgam Spaces ◽  
General Initial Data ◽  
Amalgam Spaces ◽  
Loss Of Regularity ◽  
Bbm Equation

We consider the Benjamin–Bona–Mahony (BBM) equation of the form ut+ux+uux−uxxt=0,(x,t)∈M×R where M=T or R. We establish norm inflation (NI) with infinite loss of regularity at general initial data in Fourier amalgam and Wiener amalgam spaces with negative regularity. This strengthens several known NI results at zero initial data in Hs(T) established by Bona–Dai (2017) and the ill-posedness result established by Bona–Tzvetkov (2008) and Panthee (2011) in Hs(R). Our result is sharp with respect to the local well-posedness result of Banquet–Villamizar–Roa (2021) in modulation spaces Ms2,1(R) for s≥0.

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