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Finite Central Truncations of Linear Operators

Lookup NU author(s): Professor Mihai Putinar


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© Springer International Publishing AG 2017. By interpreting the exponential orthogonal polynomials as characteristic polynomials of finite central truncations of the underlying hyponormal operator one opens a vast toolbox of Hilbert space geometry methods. In particular we prove in this chapter that trace class modifications of the hyponormal operator attached to a domain will not alter the convex hull of the support of any cluster point of the count in measures of the roots of the orthogonal polynomials. As a sharp departure from the case of complex orthogonal polynomials associated to a Lebesgue space we prove that the convex hull of these supports is not affected by taking the union of an open set with a disjoint quadrature domain. However, similar to the case of Bergman orthogonal polynomials, we prove that the exponential orthogonal polynomials satisfy a three term relation only in the case of an ellipse. Some general perturbation theory arguments are collected in the last section.

Publication metadata

Author(s): Gustafsson B, Putinar M

Publication type: Book Chapter

Publication status: Published

Book Title: Hyponormal Quantization of Planar Domains

Year: 2017

Volume: 2199

Pages: 57-75

Online publication date: 26/09/2017

Acceptance date: 02/04/2016

Series Title: Lecture Notes in Mathematics

Publisher: Springer Verlag


DOI: 10.1007/978-3-319-65810-0_5

Library holdings: Search Newcastle University Library for this item

ISBN: 9783319658100