Studies on Cauchy–Stieltjes Kernel Families

Abdulmajeed Albarrak, Raouf Fakhfakh () and Ghadah Alomani
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Abdulmajeed Albarrak: Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi Arabia
Raouf Fakhfakh: Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi Arabia
Ghadah Alomani: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Mathematics, 2025, vol. 13, issue 19, 1-19

Abstract: In the setting of Cauchy–Stieltjes kernel (CSK) families, this study provides some features of free Poisson, free Gamma, and free Binomial laws, as well as some innovative limit theorems linked to Fermi convolution. These findings highlight the fundamental links between noncommutative probability and analytic function theory, demonstrating the usefulness of CSK families for advancing the computational and theoretical aspects of free harmonic analysis.

Keywords: variance function; free Gamma law; Cauchy–Stieltjes transform; Boolean additive convolution; free additive convolution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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