Weighted polynomials and weighted pluripotential theory

By Thomas F. Bloom. 2006

48 citations recorded by the source corpus.

Let E be a compact subset of C N and w > 0 an admissible weight function on E. To (E,ω) we associate a canonical circular set Z C We obtain precise relations between the weighted pluricomplex Green function and weighted equilibrium measure of (E, w) and the pluricomplex Green function and equilibrium measure of Z. These results, combined with an appropriate form of the Bernstein-Markov inequality, are used to obtain asymptotic formulas for the leading coefficients of orthonormal polynomials with respect to certain exponentially decreasing weights in R N .

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/78411b4dcc29b718eb48e7eaa4c18254b96853b9

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In Applied Mathematics

1. Norman Levenberg
2. Thomas F. Bloom
3. Len P. Bos
4. Jean-Paul Calvi
5. Robert J. Berman
6. S. Boucksom

In Geometry and Topology

1. Norman Levenberg
2. Thomas F. Bloom
3. Len P. Bos
4. Jean-Paul Calvi

Citations in the corpus

• Polynomial Interpolation and Approximation in C^d (2011, background): “A brief introduction to weighted pluripotential theory in C is provided in section 6, and a connection with unweighted pluripotential theory in C as in [7] is given.”