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Some Separate Quasi-Asymptotics Properties of Multidimensional Distributions and Application
Pure and Applied Mathematics Journal
Volume 9, Issue 3, June 2020, Pages: 64-69
Received: Jun. 17, 2020; Accepted: Jul. 3, 2020; Published: Jul. 13, 2020
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Nenad Stojanovic, Department of Mathematics, Faculty of Agriculture, University of Banja Luka, Banja Luka, Bosnia and Herzegovina
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Quasi-asymptotic behavior of functions as a method has its application in observing many physical phenomena which are expressed by differential equations. The aim of the asymptotic method is to allow one to present the solution of a problem depending on the large (or small) parameter. One application of asymptotic methods in describing physical phenomena is the quasi-asymptotic approximation. The aim of this paper is to look at the quasi-asymptotic properties of multidimensional distributions by extracted variable. Distribution T(x0,x) from S'(Ṝ+1×Rn) has the property of the separability of variables, if it can be represented in form T(x0,x)=∑φi(x0i (x) where distributions, φi(x0) from S'(Ṝ1) and ψi from S(Rn), x0 from Ṝ1+ and x is element Rn different values of do not depend on each other. Distribution T(x0,x) the element S'(Ṝ+1×Rn) is homogeneous and of order α at variable x0 is element Ṝ1+ and x=x1,x2,…,xn from Rn if for k>0 it applies that T(kx0,kx)=kα T(x0,x). The method of separating variables is one of the most widespread methods for solving linear differential equations in mathematical physics. In this paper, the results by V. S Vladimirov are used to present the proof of the basic theorems, regarding the quasi-asymptotic behavior of multidimensional distributions by a singular variable, with the application of quasi-asymptotics to the solution of differential equations.
Distribution Spaces, Asymptotics, Separate Quasi-Asymptotics, Multidimensional Distributions
To cite this article
Nenad Stojanovic, Some Separate Quasi-Asymptotics Properties of Multidimensional Distributions and Application, Pure and Applied Mathematics Journal. Vol. 9, No. 3, 2020, pp. 64-69. doi: 10.11648/j.pamj.20200903.13
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
V. S. Vladimirov, N. Drozinov, B. I. Zavjalov, Mnogomernie Tauberovi Teoremi dlja Obobosce- nie funkcii, Nauka, Moskva, 1986.
N. Drozinov, B. I, Zavjalov, Vvedenie v teoriju oboboscenih funkcii, Mathematiceskij institut im V. A. Steklov, RAN (MIAN), Moskva. 2006.
S. Pilipović, B. Stanković, Vindas, J., Asymptotic behavior of generalizedfunctions, Series on Analysis, Applications and Computation, 5, World Sci-entific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012.
S. Pilipović, J. Toft, P seudo-Differential Operators and Genera -lized Functions, Birkhäuser; 2015.
V. S. Vladimirov, Oboboscenie funkcii u matematice skoj fizici, Nauka, 1979.
N. Y. Drozhzhinov, B. I. Zav’yalov, Asymptotically homogeneous generalized functions and boundary properties of functions holomorphic in tubularcones. Izv. Math., 70, (2006), 1117–1164.
S. Pilipović, B. Stanković, Prostori distribucija, SANU, Novi Sad, 2000.
S. Pilipović, On the Quasiasymptotic of Schwartz distributions. Math. Nachr. 141 (1988), 19-25.
J. Vindas, S. Pilipović, Structural theorems for quasiasympto- tics of distributions at the origin, Math. Nachr. 282 (2.11), (2009), 1584–1599.
J. Vindas, The structure of quasiasymptotics of Schwartz distributions, Banach Center Publ. 88 (2010), 297-31.
S. Pilipović, Quasiasymptotic and the translation asymptotic behavior of distributions, Acta Math. Hungarica, 55 (3-4) (1990), 239-243.
V. S. Vladimirov, Uravnenija mathematiceskoj fiziki, Nauke, Moskva, 1981.
Teofanov, N., Convergence of multiresolution expansion in the Schwartzclass, Math. Balcanica, 20, (2006), 101-111.
S. Pilipović, B. Stanković, Asymptotic Behavior or Generalized Function, Novi Sad, 2008.
N. Stojanović, Separirana kvaziasimptotika više-dimenzionih distribucija, PMF, Novi Sad, 2009-magistarska teza.
M. Tomić, 'Jovan Karamata 1902-1967', Bulletin T. CXXII de l’Acad´emie Serbe des Sciences et des Arts, No 26, 2001.
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