Exponential Orthogonal Polynomials

Gustafsson, B; Putinar, M

doi:10.1007/978-3-319-65810-0_4

Exponential Orthogonal Polynomials

Lookup NU author(s): Professor Mihai Putinar

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Abstract

© Springer International Publishing AG 2017. This chapter contains some initial results, obtained by direct or classical methods, on the zeros of the exponential orthogonal polynomials. For example, we estimate the decay of coefficients of orthogonal expansion by using a result of J.L. Walsh and we prove that the zeros always stay in the convex hull of the closure of the domain. In addition, we identify the zeros as also being eigenvalues of the appropriate Hessenberg matrices, and we elaborate this connection further in the case of quadrature domains.