Vilmos Totik Boeken

The book delves into the advancements in approximation theory and orthogonal polynomials, highlighting the significant solutions to previously unsolvable problems through the integration of approximation techniques with classical potential theory. It discusses the emergence of non-classical orthogonal polynomials, incomplete polynomials, and multipoint Pade approximation, along with their applications in resolving notable issues like Freud's problems and the "l/9-th" conjecture. A key objective is to offer a comprehensive introduction to weighted potential theory and its classical foundations.

This volume presents a diverse collection of problems from classical set theory, interconnected with algebra, combinatorics, topology, and real analysis. Problems are organized by difficulty, with historical context and references provided. It emphasizes the beauty of set theory, focusing on results from 1920-1970 without delving into independence methods.

Focusing on general orthogonal polynomials, this comprehensive work delves into their asymptotic behavior and the distribution of their zeros. It serves as a detailed reference for researchers and mathematicians, offering insights into the theoretical aspects and applications of these polynomials. The book aims to bridge gaps in existing literature, providing a thorough understanding of the subject for advanced study and research in mathematics.