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Summary

Starting from the explicit formulas known for simple multivariate geometries (balls, cube, simplex) the discussion moves to recent advances in pluripotential theory. The essential Bernstein-Markov property of a measure is necessary for deriving asymptotics of the Christoffel function outside the support of the generating measure, and in some fortunate situations also inside the support. A balance between strong and weak limits enters into the game.

Summary

In this chapter the basic theory of hypergeometric functions for root systems is discussed, together with some of its applications. These functions arise in various contexts such as the representation theory of reductive groups, multivariate orthogonal polynomials, harmonic analysis on symmetric spaces, integrable models in mathematical physics, Dunkl operators, Knizhnik-Zamolodchikov connections, affine Hecke algebras, algebraic combinatorics (e.g. the Macdonald conjectures), the determination of certain Bernstein-Sato polynomials and period integrals for moduli of Del Pezzo surfaces.

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4 - Multivariate Christoffel–Darboux Analysis

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8 - Jacobi Polynomials and Hypergeometric Functions Associated with Root Systems

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2 results

4 - Multivariate Christoffel–Darboux Analysis

Summary

8 - Jacobi Polynomials and Hypergeometric Functions Associated with Root Systems

Summary