A compactness criterion for translation invariant Banach spaces of functions

1982 ◽  
Vol 8 (3) ◽  
pp. 165-172 ◽  
Author(s):  
H. G. Feichtinger
Keyword(s):  
Banach Spaces ◽  
Compactness Criterion ◽  
Translation Invariant

scholarly journals Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces

2016 ◽  
Vol 56 (2) ◽  
pp. 401-440 ◽  
Author(s):  
Pavel Dimovski ◽  
Stevan Pilipović ◽  
Bojan Prangoski ◽  
Jasson Vindas
Keyword(s):  
Banach Spaces ◽  
Translation Invariant

Multipliers for vector valued functions

1984 ◽  
Vol 99 (1-2) ◽  
pp. 137-143
Author(s):  
José Luis Torrea
Keyword(s):  
Abelian Group ◽  
Banach Spaces ◽  
Compact Abelian Group ◽  
Locally Compact Abelian Group ◽  
Lebesgue Spaces ◽  
Locally Compact ◽  
Translation Invariant ◽  
Bounded Linear ◽  
Vector Valued Functions ◽  
Vector Valued

SynopsisLet G be a locally compact abelian group and let Γ be the dual of G. Let A, B be Banach spaces and Lp(G,A) the Bochner-Lebesgue spaces. We prove that the space of bounded linear translation invariant operators from L1(G, A) to LX(G, B) can be identified with the space of bounded convolution invariant (in some sense) operators and also with the space of a(A, B)-valued “weak regular” measures with the relation Tf = f *μ. (A. The existence of a function m∈ L∞ (Γ,α(A,B)), such that is also proved.

scholarly journals On the mild solutions of higher-order differential equations in Banach spaces

2003 ◽  
Vol 2003 (15) ◽  
pp. 865-880 ◽  
Author(s):  
Nguyen Thanh Lan
Keyword(s):  
Differential Equation ◽  
Banach Spaces ◽  
Mild Solutions ◽  
Higher Order ◽  
Almost Periodicity ◽  
Abstract Differential Equation ◽  
Translation Invariant ◽  
Definition Of ◽  
Translation Invariant Subspace ◽  
Higher Order Differential Equations

For the higher-order abstract differential equationu(n)(t)=Au(t)+f(t),t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspaceℳofBUC(ℝ,E)with respect to the above-mentioned equation in terms of solvability of the operator equationAX−X𝒟n=C. As applications, periodicity and almost periodicity of mild solutions are also proved.

scholarly journals New distribution spaces associated to translation-invariant Banach spaces

2014 ◽  
Vol 177 (4) ◽  
pp. 495-515 ◽  
Author(s):  
Pavel Dimovski ◽  
Stevan Pilipović ◽  
Jasson Vindas
Keyword(s):  
Banach Spaces ◽  
Translation Invariant ◽  
Distribution Spaces ◽  
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