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The Cauchy Exponential of Linear Functionals on the Linear Space of Polynomials

Author

Listed:
  • Francisco Marcellán

    (Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
    These authors contributed equally to this work.)

  • Ridha Sfaxi

    (Faculty of Sciences of Gabes, University of Gabes, 6072 Gabes, Tunisia
    These authors contributed equally to this work.)

Abstract

In this paper, we introduce the notion of the Cauchy exponential of a linear functional on the linear space of polynomials in one variable with real or complex coefficients using a functional equation by using the so-called moment equation. It seems that this notion hides several properties and results. Our purpose is to explore some of these properties and to compute the Cauchy exponential of some special linear functionals. Finally, a new characterization of the positive-definiteness of a linear functional is given.

Suggested Citation

  • Francisco Marcellán & Ridha Sfaxi, 2023. "The Cauchy Exponential of Linear Functionals on the Linear Space of Polynomials," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1895-:d:1125442
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