Optimal codomains for the Laplace operator and the product Laplace operator

被引：1
|
作者：
Alvarez, Josefina [1 ]
Moyo, Lloyd Edgar S.
机构：
[1] New Mexico State Univ, Dept Math, Las Cruces, NM 88003 USA
[2] Sul Ross State Univ, Dept Math, Alpine, TX 79832 USA
来源：
JOURNAL OF FUNCTION SPACES AND APPLICATIONS | 2007年 / 5卷 / 03期
关键词：
s'-convolution; Laplace operator and product Laplace; operator; weighted distribution spaces;
D O I：
10.1155/2007/257051
中图分类号：
学科分类号：
摘要：
An optimal codomain for an operator P (a) with fundamental solution E, is a maximal space of distributions T for which it is possible to define the convolution E * T and thus to solve the equation P (0) S = T. We identify optimal codomains for the Laplace operator in the Euclidean case and for the product Laplace operator in the product domain case. The convolution is understood in the sense of the S'-convolution.
引用
收藏
页码：269 / 285
页数：17
相关论文
共 50 条
  • [1] LAPLACE OPERATOR
    DAVIS, HF
    AMERICAN JOURNAL OF PHYSICS, 1964, 32 (04) : 318 - +
  • [2] Optimal Partitions for First Eigenvalues of the Laplace Operator
    Bozorgnia, Farid
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2015, 31 (03) : 923 - 949
  • [3] The standard Laplace operator
    Semmelmann, Uwe
    Weingart, Gregor
    MANUSCRIPTA MATHEMATICA, 2019, 158 (1-2) : 273 - 293
  • [4] The standard Laplace operator
    Uwe Semmelmann
    Gregor Weingart
    manuscripta mathematica, 2019, 158 : 273 - 293
  • [5] ON THE DISCRETIZATION OF LAPLACE OPERATOR
    ALGAZIN, SD
    DOKLADY AKADEMII NAUK SSSR, 1982, 266 (03): : 521 - 525
  • [6] The estimates of eigenvalues for Laplace operator
    Deng, YB
    DIFFERENTIAL EQUATIONS AND CONTROL THEORY, 1996, 176 : 15 - 20
  • [7] ABOUT THE SPECTRUM OF THE LAPLACE OPERATOR
    Biyarov, B. N.
    EURASIAN MATHEMATICAL JOURNAL, 2011, 2 (02): : 129 - 133
  • [8] On the attainable eigenvalues of the Laplace operator
    Bucur, D
    Buttazzo, G
    Figueiredo, I
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1999, 30 (03) : 527 - 536
  • [9] INVERSE PROBLEM FOR LAPLACE OPERATOR
    SCHULZE, BW
    MATHEMATISCHE NACHRICHTEN, 1975, 67 : 225 - 235
  • [10] The Higher Spin Laplace Operator
    De Bie, Hendrik
    Eelbode, David
    Roels, Matthias
    POTENTIAL ANALYSIS, 2017, 47 (02) : 123 - 149
12345