By car
Cassie Mayer
Each book in this series examines one mode of transport in order to introduce the reader to how people around the world get from place to place.
Read Time: ~4.2 hr
General orthogonal polynomials
by Herbert Stahl, Vilmos Totik (1992)
About this book
In this treatise, the authors present the general theory of orthogonal polynomials on the complex plane and several of its applications. The assumptions on the measure of orthogonality are general, the only restriction is that it has compact support on the complex plane. In the development of the theory the main emphasis is on asymptotic behaviour and the distribution of zeros. In the following chapters, the author explores the exact upper and lower bounds are given for the orthonormal polynomials and for the location of their zeros; regular n-th root asymptotic behaviour; and applications of the theory, including exact rates for convergence of rational interpolants, best rational approximants and non-diagonal Pade approximants to Markov functions (Cauchy transforms of measures). The results are based on potential theoretic methods, so both the methods and the results can be extended to extremal polynomials in norms other than L2 norms. A sketch of the theory of logarithmic potentials is given in an appendix.
Setting / LocationGlobal
Story EraModern Era
Protagonist / CoreGeneral orthogonal polynomials Lead Character
Themes & Moods
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