电邮这篇文章 Tauberian class estimates for vector-valued distributions
- 作者: Pilipović S.R.1, Vindas J.2
-
隶属关系:
- University of Novi Sad, Faculty of Science and Mathematics, Department of Mathematics and Informatics
- Ghent University
- 期: 卷 210, 编号 2 (2019)
- 页面: 115-142
- 栏目: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/133265
- DOI: https://doi.org/10.4213/sm9061
- ID: 133265
如何引用文章
开放存取
##reader.subscriptionAccessGranted##
订阅存取
详细
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.
作者简介
Stevan Pilipović
University of Novi Sad, Faculty of Science and Mathematics, Department of Mathematics and Informatics
Email: pilipovic@unsim.ns.ac.yu
Doctor of physico-mathematical sciences, Professor
Jasson Vindas
Ghent University
Email: jasson.vindas@ugent.be
PhD, Professor
参考
- N. H. Bingham, C. M. Goldie, J. L. Teugels, Regular variation, Encyclopedia Math. Appl., 27, Paperback ed., Cambridge Univ. Press, Cambridge, 1989, xx+494 pp.
- R. Chill, “Tauberian theorems for vector-valued Fourier and Laplace transforms”, Studia Math., 128:1 (1998), 55–69
- G. Debruyne, J. Vindas, “Generalization of the Wiener–Ikehara theorem”, Illinois J. Math., 60:2 (2016), 613–624
- G. Debruyne, J. Vindas, “Optimal Tauberian constant in Ingham's theorem for Laplace transforms”, Israel J. Math., 228:2 (2018), 557–586
- G. Debruyne, J. Vindas, “Complex Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior”, J. Anal. Math. (to appear)
- P. Dimovski, S. Pilipovic, J. Vindas, “New distribution spaces associated to translation-invariant Banach spaces”, Monatsh. Math., 177:4 (2015), 495–515
- Ю. Н. Дрожжинов, “Многомерные тауберовы теоремы для обобщенных функций”, УМН, 71:6(432) (2016), 99–154
- Ю. Н. Дрожжинов, Б. И. Завьялов, “Тауберовы теоремы для обобщенных функций со значениями в банаховых пространствах”, Изв. РАН. Сер. матем., 66:4 (2002), 47–118
- Ю. Н. Дрожжинов, Б. И. Завьялов, “Многомерные тауберовы теоремы для обобщенных функций со значениями в банаховых пространствах”, Матем. сб., 194:11 (2003), 17–64
- Ю. Н. Дрожжинов, Б. И. Завьялов, “Применения тауберовых теорем в некоторых задачах математической физики”, ТМФ, 157:3 (2008), 373–390
- M. Holschneider, Wavelets. An analysis tool, Oxford Math. Monogr., The Clarendon Press, Oxford Univ. Press, New York, 1995, xiv+423 pp.
- J. Korevaar, Tauberian theory. A century of developments, Grundlehren Math. Wiss., 329, Springer-Verlag, Berlin, 2004
- J. Korevaar, “Distributional Wiener–Ikehara theorem and twin primes”, Indag. Math. (N.S.), 16:1 (2005), 37–49
- S. Pilipovic, D. Rakic, J. Vindas, “New classes of weighted Hölder–Zygmund spaces and the wavelet transform”, J. Funct. Spaces Appl., 2012 (2012), 815475, 18 pp.
- S. Pilipovic, B. Stankovic, J. Vindas, Asymptotic behavior of generalized functions, Ser. Anal. Appl. Comput., 5, World Sci. Publ., Hackensack, NJ, 2012, xiv+294 pp.
- S. Pilipovic, J. Vindas, “Multidimensional Tauberian theorems for vector-valued distributions”, Publ. Inst. Math. (Beograd) (N.S.), 95:109 (2014), 1–28
- У. Рудин, Функциональный анализ, Мир, М., 1975, 443 с.
- L. Schwartz, “Theorie des distributions à valeurs vectorielles. I”, Ann. Inst. Fourier Grenoble, 7 (1957), 1–141
- J. Sebastião e Silva, “Sur la definition et la structure des distributions vectorielles”, Portugal. Math., 19 (1960), 1–80
- F. Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York–London, 1967, xvi+624 pp.
- J. Vindas, S. Pilipovic, D. Rakic, “Tauberian theorems for the wavelet transform”, J. Fourier Anal. Appl., 17:1 (2011), 65–95
- V. S. Vladimirov, Methods of the theory of generalized functions, Anal. Methods Spec. Funct., 6, Taylor & Francis, London, 2002, xiv+311 pp.
- В. С. Владимиров, Ю. Н. Дрожжинов, Б. И. Завьялов, Многомерные тауберовы теоремы для обобщенных функций, Наука, М., 1986, 304 с.
- Б. И. Завьялов, “Об асимптотических свойствах функций, голоморфных в трубчатых конусах”, Матем. сб., 136(178):1(5) (1988), 97–114
补充文件
