On the neutral Hermite product of the distributions x±n and δ(m)(x)

被引：1

作者：

Shen, Chun ^{[1
]}

Sun, Meina ^{[1
]}

机构：

[1] Ludong Univ, Sch Math & Informat, Yantai, Peoples R China

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2008年 / 19卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Hermite function; Hermite expansions; product of distributions;

D O I：

10.1080/10652460701880094

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce the neutral Hermite product and study products of tempered distributions based on the Hermite expansions. In particular, we consider products of distributions x(n) and d(m)(x) by using the neutral Hermite product and the results are identical with the classical theory of Schwartz distributions. Finally, the recurrence relations about the Hermite expansion coefficients of x(+/-n) delta((m))(x) are obtained for the numerical computation.

引用

页码：387 / 398

页数：12

共 50 条

[21] THE ELEMENTARY SOLUTIONS OF LAPLACIAN OPERATOR ITERATED m TIMES Delta(m){u(x(1,...)x(n)}= f(x(1,...)x(n)}
Aguirre, Manuel A.
Aguirre, Emilio A.
NEXO REVISTA CIENTIFICA, 2014, 27 (01): : 46 - 59
[22] On the rational difference equation x(n) = 1+ (1-x(n-k))(1-x(n-l))(1-x(n-m)) / x(n-k)+x(n-l)+x(n-m)
Liao, Maoxin
Tang, Xianhua
Xu, Changjin
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2011, 35 (1-2) : 63 - 71
[23] OSCILLATORY SOLUTIONS OF EQUATION Y'(X)=M(X)Y(X-N(X))
LILLO, JC
JOURNAL OF DIFFERENTIAL EQUATIONS, 1969, 6 (01) : 1 - &
[24] Heinz mean curvature estimates in warped product spaces M x e N
Salavessa, Isabel M. C.
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2018, 53 (02) : 265 - 281
[25] PRODUCT OF DISTRIBUTIONS X-R-1/2(+) AND X-R-1/2(-)
FISHER, B
PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1972, 71 (JAN): : 123 - &
[26] THE NON-COMMUTATIVE NEUTRIX PRODUCT OF THE DISTRIBUTIONS X+(-R) AND DELTA(P) (X)
FISHER, B
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1983, 14 (12): : 1439 - 1449
[27] On the non-commutative neutrix product of the distributions xr lnp |x| and xs lnq |x|
Fisher, Brian
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2008, 19 (11) : 801 - 807
[28] On the non-commutative neutrix product of the distributions xr lnP | x | and x-s
Fisher, B
Tas, K
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2005, 16 (02) : 131 - 138
[29] Classification of the entangled states 2 x M x N
Li, Jun-Li
Qiao, Cong-Feng
QUANTUM INFORMATION PROCESSING, 2013, 12 (01) : 251 - 268
[30] SOLUTION OF EQUATION AX + XB = C BY INVERSION OF AN M X M OR N X N MATRIX
JAMESON, A
SIAM JOURNAL ON APPLIED MATHEMATICS, 1968, 16 (05) : 1020 - &

← 1 2 3 4 5 →