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Abstract We extend the free convolution of Brown measures of $$R$$-diagonal elements introduced by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions.
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On the sharp constants in the regional fractional Sobolev inequalities
Abstract In this paper, we study the sharp constants in fractional Sobolev inequalities associated with the regional fractional Laplacian in domains.
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- Award ID(s):
- 1954995
- PAR ID:
- 10628074
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Partial Differential Equations and Applications
- Volume:
- 6
- Issue:
- 2
- ISSN:
- 2662-2963
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1007/s42985-025-00317-2
