Laplace transform in spaces of ultradistributions
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The Laplace transform in Komatsu ultradistributions is considered in this paper, where conditions are given under which an analytic function is a Laplace transformation of an ultradimensional distribution.Abstract:
The Laplace transform in Komatsu ultradistributions is considered Also, conditions are given under which an analytic function is a Laplace transformation of an ultradistributionread more
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Pseudodifferential operators of infinite order in spaces of tempered ultradistributions
TL;DR: In this paper, specific global symbol classes and corresponding pseudodifferential operators of infinite order that act continuously on the space of tempered ultradistributions of Beurling and Roumieu type are constructed.
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On quasianalytic classes of Gelfand–Shilov type. Parametrix and convolution
TL;DR: In this paper, a convolution theory for quasianalytic ultradistributions of Gelfand-Shilov type was developed for Fourier hyperfunctions and Fourier ultra-hyperfunctions.
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Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces
TL;DR: In this paper, the authors introduced and studied a number of new spaces of ultradifferentiable functions and ultradistributions and applied their results to the study of the convolution of ultradicributions.
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On weighted inductive limits of spaces of ultradifferentiable functions and their duals
Andreas Debrouwere,Jasson Vindas +1 more
TL;DR: In this paper, the completeness of two general classes of weighted inductive limits of spaces of ultradifferentiable functions is discussed and their duals are characterized in terms of the growth of convolution averages of their elements.
Gelfand-Shilov spaces and localization operators
TL;DR: In this paper, Komatsu's approach is used to study Gelfand-Shilov spaces of ultradifferentiable functions in both quasianalytic and non-quasianallytic case.
References
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Book
Théorie des distributions
TL;DR: The merite as discussed by the authors is a date marque une date dans le progres des mathematiques and de la physique en levant l'ambiguite que constituait le succes des methodes de calcul symbolique aupres des physiciens and l'inacceptabilite de leurs formules au regard de la rigueur mathematiques.
Journal ArticleDOI
Characterizations of bounded sets in spaces of ultradistributions
TL;DR: In this article, bounded sets in ultradistributions spaces were characterized via convolution by corresponding test functions, and structural theorems for L/{MP} and -'f{MP t E [}, oo were also given.