Characterizations of bounded sets in spaces of ultradistributions

Author:

Pilipović Stevan

Abstract

We characterize bounded sets in ultradistributions spaces D L t ( M p ) , t [ 1 , ] , S { M p } \mathcal {D}_{{L^t}}^{’({M_p})},\,t \in [1,\infty ],\,S{’^{\{ {M_p}\} }} , and S ( M p ) S{’^{({M_p})}} and bounded sets and convergent sequences in D ( M p ) \mathcal {D}{’^{({M_p})}} and D { M p } \mathcal {D}{’^{\{ {M_p}\} }} via the convolution by corresponding test functions. The structural theorems for D L t { M p } \mathcal {D}_{{L^t}}^{’\{ {M_p}\} } and D ~ L t { M p } , t [ 1 , ] \widetilde D_{{L^t}}^{’\{ {M_p}\} },\;t \in [1,\infty ] , are also given.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference12 articles.

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