Logarithmic Potentials with External Fields

Part 1 Fundamentals. I Weighted Potentials.- II Recovery of Measures, Green Functions and Balayage.- III Weighted Polynomials.- IV Determination of the Extremal Measure.- Part 2 Applications and Generalizations.- V Extremal Point Methods.- VI Weights on the Real Line.- VII Applications Concerning Orthogonal Polynomials.- VIII Signed Measures.- IX Some Problems from Physics.- X Generalizations.- Part 3 Appendices.- A.I Basic Tools.- A.II The Dirichlet Problem and Harmonic Measures.- A.III Weighted approximation in ??.- A.IV Classical Logarithmic Potential Theory.

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• Análise numérica
• Análise complexa, variáveis ??complexas
• Cálculo diferencial e equações
• Análise funcional e transforma

Potential theory;logarithmic potentials;approximation theory;capacity;external fields;extremal points;polynomial approximation with varying weight;extremum problems;orthogonal polynomials;energy integrals;signed measures;weighted polynomials;weighted Fekete points;weighted Leja points;equilibrium measures