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This article is cited in 5 scientific papers (total in 5 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.
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
Linking options:
https://www.mathnet.ru/eng/sm9061https://doi.org/10.1070/SM9061 https://www.mathnet.ru/eng/sm/v210/i2/p115
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Abstract page: | 358 | Russian version PDF: | 30 | English version PDF: | 7 | References: | 32 | First page: | 9 |
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