scholarly journals Completeness of shifted dilates in invariant Banach spaces of tempered distributions

2021 ◽  
pp. 1
Author(s):  
Hans G. Feichtinger ◽  
Anupam Gumber
Keyword(s):  
Banach Spaces ◽  
Tempered Distributions

Splitting of the +' Space into a Union of Banach Spaces through Laguerre Expansions

2006 ◽  
Vol 6 (3) ◽  
pp. 336-344 ◽  
Author(s):  
M. Stojanović
Keyword(s):  
Banach Spaces ◽  
Laguerre Expansions ◽  
Tempered Distributions

AbstractWe split the space of tempered distributions into a union of Banach spaces with respect to the scale of spaces, which allows us to give the approximation of the generalization of function therein.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

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