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

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URI: https://hdl.handle.net/10016/39081
ISSN: 2227-7390
DOI: https://doi.org/10.3390/math11081895
UXXI: AR/0000033519
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cauchy_MATHEMATICS_2023.pdf (366.06 KB)
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2023-04-02
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MDPI
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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.
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Cauchy exponential of linear functional, Cauchy power of linear functional, Du-Laguerre-Hahn operator, Orthogonal polynomial sequence, Positive-definite linear functional, Regular linear functional, Weakly-regular linear functional
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Marcellán, F., & Sfaxi, R. (2023). The Cauchy exponential of linear functionals on the linear space of polynomials. Mathematics, 11(8), 1895.
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