Mehler-Fock transforms of generalized functions via the method of adjoints

被引：12
|
作者：
Gonzalez, BJ [1 ]
Negrin, ER [1 ]
机构：
[1] Univ La Laguna, Dept Anal Matemat, La Laguna 38271, Spain
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1997年 / 125卷 / 11期
关键词：
Mehler-Fock transform; Legendre function; generalized functions; distributions of compact support; Paley-Wiener type theorem;
D O I：
10.1090/S0002-9939-97-03957-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we analyse the Mehler-Fock transform of generalized functions via the method of adjoints. For a distribution of compact support, we prove that its Mehler-Fock transform agrees with its transform via the kernel method. A Paley-Wiener type theorem is established.
引用
收藏
页码：3243 / 3253
页数：11
相关论文
共 50 条
  • [31] Characterization of Weyl operator in terms of Mehler-Fock transform
    Verma, Sandeep Kumar
    Prasad, Akhilesh
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (15) : 9119 - 9128
  • [32] Heat Kernel in the Framework of Zero Order Mehler-Fock Transform
    Prasad, Akhilesh
    Verma, Sandeep Kumar
    COMPLEX ANALYSIS AND OPERATOR THEORY, 2019, 13 (07) : 3235 - 3249
  • [33] Localization Operators and Scalogram in the Framework of Mehler-Fock Wavelet Transform
    Dades, Abdelaali
    Tyr, Othman
    Daher, Radouan
    Fantasse, Yassine
    COMPLEX ANALYSIS AND OPERATOR THEORY, 2023, 17 (08)
  • [34] The order Mehler-Fock transform and allied pseudo-differential operator
    Prasad, Akhilesh
    Mandal, U. K.
    Ranjan, Sudhanshu
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2025, 36 (03) : 163 - 175
  • [35] SPHERICAL-FUNCTIONS ON THE QUANTUM GROUP SU(1, 1) AND THE Q-ANALOG OF THE MEHLER-FOCK FORMULA
    VAKSMAN, LL
    KOROGODSKII, LI
    FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1991, 25 (01) : 48 - 49
  • [36] An operational calculus for a Mehler-Fock type index transform on distributions of compact support
    Srivastava, H. M.
    Gonzalez, B. J.
    Negrin, E. R.
    REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2023, 117 (01)
  • [37] A new class of Abelian theorems for the Mehler–Fock transforms
    H. M. Srivastava
    B. J. González
    E. R. Negrín
    Russian Journal of Mathematical Physics, 2017, 24 : 124 - 126
  • [38] ZERO-ORDER MEHLER-FOCK TRANSFORM AND SOBOLEV-TYPE SPACE
    Prasad, Akhilesh
    Mandal, U. K.
    Verma, S. K.
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2019, 22 (02): : 761 - 775
  • [39] An operational calculus for a Mehler-Fock type index transform on distributions of compact support
    H. M. Srivastava
    B. J. González
    E. R. Negrín
    Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2023, 117
  • [40] Erratum to “A new class of Abelian theorems for the Mehler–Fock transforms”
    H. M. Srivastava
    B. J. González
    E. R. Negrín
    Russian Journal of Mathematical Physics, 2017, 24 : 278 - 278
12345