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Tauberian class estimates for vector-valued distributions

(2019) SBORNIK MATHEMATICS. 210(2). p.272-296
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Abstract
We study Tauberian properties of regularizing transforms of vector-valued tempered distributions. The transforms have the form M-phi(f) (x, y) = (f * phi(y))(x), where the kernel phi is a test function and phi(y)(center dot) = y(-n)phi(center dot/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-phi(f)(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 phi for which these Tauberian results hold.
Keywords
regularizing transforms, class estimates, Tauberian theorems, vector-valued distributions, wavelet transform, THEOREMS

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Please use this url to cite or link to this publication:

MLA
Pilipović, Stevan, and Jasson Vindas Diaz. “Tauberian Class Estimates for Vector-valued Distributions.” SBORNIK MATHEMATICS 210.2 (2019): 272–296. Print.
APA
Pilipović, S., & Vindas Diaz, J. (2019). Tauberian class estimates for vector-valued distributions. SBORNIK MATHEMATICS, 210(2), 272–296.
Chicago author-date
Pilipović, Stevan, and Jasson Vindas Diaz. 2019. “Tauberian Class Estimates for Vector-valued Distributions.” Sbornik Mathematics 210 (2): 272–296.
Chicago author-date (all authors)
Pilipović, Stevan, and Jasson Vindas Diaz. 2019. “Tauberian Class Estimates for Vector-valued Distributions.” Sbornik Mathematics 210 (2): 272–296.
Vancouver
1.
Pilipović S, Vindas Diaz J. Tauberian class estimates for vector-valued distributions. SBORNIK MATHEMATICS. 2019;210(2):272–96.
IEEE
[1]
S. Pilipović and J. Vindas Diaz, “Tauberian class estimates for vector-valued distributions,” SBORNIK MATHEMATICS, vol. 210, no. 2, pp. 272–296, 2019.
@article{8613374,
  abstract     = {We study Tauberian properties of regularizing transforms of vector-valued tempered distributions. The transforms have the form M-phi(f) (x, y) = (f * phi(y))(x), where the kernel phi is a test function and phi(y)(center dot) = y(-n)phi(center dot/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-phi(f)(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 phi for which these Tauberian results hold.},
  author       = {Pilipović, Stevan and Vindas Diaz, Jasson},
  issn         = {1064-5616},
  journal      = {SBORNIK MATHEMATICS},
  keywords     = {regularizing transforms,class estimates,Tauberian theorems,vector-valued distributions,wavelet transform,THEOREMS},
  language     = {eng},
  number       = {2},
  pages        = {272--296},
  title        = {Tauberian class estimates for vector-valued distributions},
  url          = {http://dx.doi.org/10.1070/sm9061},
  volume       = {210},
  year         = {2019},
}

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