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Mat. Sb., 2019, Volume 210, Number 2, Pages 115–142 (Mi msb9061)  

This article is cited in 2 scientific papers (total in 2 papers)

Tauberian class estimates for vector-valued distributions

S. Pilipovića, J. Vindasb

a Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia
b Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

Abstract: We study Tauberian properties of regularizing transforms of vector-valued tempered distributions. The transforms have the form $M^\mathbf f_\varphi(x,y)=(\mathbf f\ast\varphi_y)(x)$, where the kernel $\varphi$ is a test function and $\varphi_y(\cdot)=y^{-n}\varphi(\cdot/y)$. We investigate conditions which ensure that a distribution that a priori takes values in a locally convex space actually takes values in a narrower Banach space. Our goal is to characterize spaces of Banach-space-valued tempered distributions in terms of so-called class estimates for the transform $M^\mathbf f_\varphi(x,y)$. Our results generalize and improve earlier Tauberian theorems due to Drozhzhinov and Zav'yalov. Special attention is paid to finding the optimal class of kernels $\varphi$ for which these Tauberian results hold.
Bibliography: 24 titles.

Keywords: regularizing transforms, class estimates, Tauberian theorems, vector-valued distributions, wavelet transform.

Funding Agency Grant Number
Ministry of Education, Science and Technical Development of Serbia 174024
Ghent University BOF-grant 01N01014
S. Pilipović's research was carried out with the support of the Ministarstvo Prosvete, Nauke i Tehnološkog Razvoja Republike Srbije (grant 174024). J. Vindas's research was carried out with the support of Universiteit Gent (BOF-grant 01N01014).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm9061

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English version:
Sbornik: Mathematics, 2019, 210:2, 272–296

Bibliographic databases:

UDC: 517.53
MSC: Primary 40E05, 46F05; Secondary 46F12
Received: 05.01.2018

Citation: S. Pilipović, J. Vindas, “Tauberian class estimates for vector-valued distributions”, Mat. Sb., 210:2 (2019), 115–142; Sb. Math., 210:2 (2019), 272–296

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Neyt L. Vindas J., “A Multidimensional Tauberian Theorem For Laplace Transforms of Ultradistributions”, Integral Transform. Spec. Funct.  crossref  mathscinet  isi
    2. Pilipovic S., Rakic D., Teofanov N., Vindas J., “Multiresolution Expansions and Wavelets in Gelfand-Shilov Spaces”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 114:2 (2020)  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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