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The Lambert transform over distributions of compact support, \(L^1\)-functions and Boehmian spaces

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Abstract

In this paper, we study the Lambert transform over distributions of compact support on \((0,\infty )\). We obtain an inversion formula for this transform and we prove a Parseval-type relation for the Lambert transform of functions in \(L^1 ((0,\infty ))\). We also extend this transform to Boehmian spaces.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de La Laguna (ULL), Campus de Anchieta, 38271, La Laguna, Tenerife, Spain

    Benito J. González & Emilio R. Negrín

  2. Department of Mathematics, Central University of Tamil Nadu, Thiruvarur, 610101, India

    R. Roopkumar

Authors
  1. Benito J. González
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  2. Emilio R. Negrín
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  3. R. Roopkumar
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Corresponding author

Correspondence to Benito J. González.

Additional information

Communicated by Sorina Barza.

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González, B.J., Negrín, E.R. & Roopkumar, R. The Lambert transform over distributions of compact support, \(L^1\)-functions and Boehmian spaces. Ann. Funct. Anal. 12, 16 (2021). https://doi.org/10.1007/s43034-020-00103-8

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  • DOI: https://doi.org/10.1007/s43034-020-00103-8

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