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Finite Central Truncations of Linear Operators
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2017 (English)In: Hyponormal Quantization of Planar Domains: Exponential Transform in Dimension Two, Springer, 2017, Vol. 2199, p. 57-75Chapter in book (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer, 2017. Vol. 2199, p. 57-75
Series
Lecture Notes in Mathematics, ISSN 0075-8434 ; 2199
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-215902DOI: 10.1007/978-3-319-65810-0_5Scopus ID: 2-s2.0-85030679344ISBN: 978-3-319-65809-4 (print)OAI: oai:DiVA.org:kth-215902DiVA, id: diva2:1149789
Note

QC 20171017

Available from: 2017-10-17 Created: 2017-10-17 Last updated: 2017-10-17Bibliographically approved

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