FUNCTIONAL EQUATIONS IN SCHWARTZ DISTRIBUTIONS AND THEIR STABILITIES

被引：0

作者：

Chung, Jae-Young ^{[1
]}

机构：

[1] Kunsan Natl Univ, Dept Math, Kunsan 573701, South Korea

来源：

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2009年 / 3卷 / 01期

关键词：

d'Alembert equation; Pompeiu equation; logarithmic functional equation; distribution; Hyers-Ulam stability;

D O I：

10.2298/AADM0901014C

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Employing two methods we consider a class of n-dimensional functional equations in the space of Schwartz distributions. As the first approach,employing regularizing functions we reduce the equations in distributions to classical ones of smooth functions and find the solutions. Secondly, using differentiation in distributions,converting the functional equations to differential equations and find the solutions. Also we consider the HYERS-ULAM stability of the equations.

引用

下载

页码：14 / 26

页数：13

共 50 条

[41] APPROXIMATELY CONVEX SCHWARTZ DISTRIBUTIONS
Chung, Jae-Young
JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, 2009, 16 (02): : 179 - 186
[42] Approximately additive Schwartz distributions
Chung, Jaeyoung
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 324 (02) : 1449 - 1457
[43] Cohomologies of spaces of Schwartz distributions
Zharinov, V. V.
THEORETICAL AND MATHEMATICAL PHYSICS, 2012, 172 (01) : 879 - 884
[44] THE HILBERT TRANSFORM OF SCHWARTZ DISTRIBUTIONS
PANDEY, JN
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 89 (01) : 86 - 90
[45] BANACH SPACES FOR THE SCHWARTZ DISTRIBUTIONS
Gill, Tepper L.
REAL ANALYSIS EXCHANGE, 2018, 43 (01) : 1 - 36
[46] DIFFERENTIAL OPERATORS ON SCHWARTZ DISTRIBUTIONS
Sardanashvily, G.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2012, 9 (07)
[47] Wavelet Transforms of Schwartz Distributions
Pandey, J. N.
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2011, 13 (01) : 47 - 83
[48] POINTWISE KERNELS OF SCHWARTZ DISTRIBUTIONS
TODOROV, T
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 114 (03) : 817 - 819
[49] Various generalized Ulam-Hyers stabilities of a nonic functional equations
Rassias, John M.
Arunkumar, M.
Sathya, E.
Namachivayam, T.
TBILISI MATHEMATICAL JOURNAL, 2016, 9 (01): : 159 - 196
[50] Enhanced zeta distributions and its functional equations
Nishiyama, Kyo
Rsted, Bent
Wachi, Akihito
32ND INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN PHYSICS (GROUP32), 2019, 1194

← 1 2 3 4 5 →