Log-convexity unifies and extends majorization inequalities to Macdonald, Jack, and Heckman-Opdam hypergeometric functions, resolving open conjectures.
An introduction to Dunkl theory and its analytic aspects
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abstract
Dunkl theory is a far reaching generalization of Fourier analysis and special function theory related to root systems. During the sixties and seventies, it became gradually clear that radial Fourier analysis on rank one symmetric spaces was closely connected with certain classes of special functions in one variable. During the eighties, several attempts were made, mainly by the Dutch school, to extend these results in higher rank (i.e. in several variables), until the discovery of Dunkl operators in the rational case and Cherednik operators in the trigonometric case. Together with q-special functions introduced by Macdonald, this has led to a beautiful theory, developed by several authors, which encompasses in a unified way harmonic analysis on all Riemannian symmetric spaces and spherical functions thereon.In this series of lectures, delivered at the Summer School AAGADE 2015 (Analytic, Algebraic and Geometric Aspects of Differential Equations, Mathematical Research and Conference Center, Bedlewo, Poland, September 2015), we aim at giving an updated overview of Dunkl theory, with an emphasis on its analytic aspects.
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UNVERDICTED 2representative citing papers
Introduces and studies the rectangular finite free heat flow as a dynamical system on polynomials with equivalent characterizations, root asymptotics, and connections to Calogero-Moser systems and mean curvature flow on Lie group orbits.
citing papers explorer
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Majorization Inequalities from Logarithmic Convexity
Log-convexity unifies and extends majorization inequalities to Macdonald, Jack, and Heckman-Opdam hypergeometric functions, resolving open conjectures.
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The Rectangular Finite Free Heat Flow
Introduces and studies the rectangular finite free heat flow as a dynamical system on polynomials with equivalent characterizations, root asymptotics, and connections to Calogero-Moser systems and mean curvature flow on Lie group orbits.