A relationship between the algebraic multiplicity of eigenvalues of fractional integral operators and the simplicity of zeros of Mittag–Leffler functions

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Abstract

In this short note, we establish a connection between the algebraic multiplicity of eigenvalues of compact integral operators and the simplicity of zeros of a class of the Mittag–Leffler functions E_α,α(z) and E_α,2(z) for 1 < α < 2. Although these are two seemingly unrelated concepts in mathematics, our approach provides a functional-analytic criterion for determining the simplicity of zeros in this class of Mittag–Leffler functions.

Keywords

algebraic simplicity / fractional Sturm–Liouville / Mittag–Leffler function / simplicity of zeros

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