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Regularity Properties of Free Multiplicative Convolution on the Positive Line by Ji, Hong Chang is a scholarly article available to read on EtoBox.

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Given two nondegenerate Borel probability measures $\mu$ and $\nu$ on $\mathbb{R}_{+}=[0,\infty)$, we prove that their free multiplicative convolution $\mu\boxtimes\nu$ has zero singular continuous part and its absolutely continuous part has a density bounded by $x^{-1}$. When $\mu$ and $\nu$ are compactly supported Jacobi measures on $(0,\infty)$ having power law behavior with exponents in $(-1,1)$, we prove that $\mu\boxtimes\nu$ is another Jacobi measure whose density has square root decay at the edges of its support.

Author

Ji, Hong Chang

Published

2019

Language

EN