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Mother Bodies
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, p. 77-92Chapter in book (Refereed)
Abstract [en]

We outline the general theory for a certain kind of potential theoretic skeletons, or ‘mother bodies’, associated to a given domain. The hope is, generally speaking, that such skeletons can be identified as attractors for zeros of orthogonal polynomials, and in a few cases such expectations have indeed been met, theoretically and/or experimentally. For the exponential polynomials the success is rather limited so far, but by building in enough flexibility in the models one expects in some not so distant future to reach a reasonable matching. In the present chapter we set up desirable properties (formulated as ‘axioms’) to be satisfied by mother bodies. Since the search for potential theoretic skeletons is a highly ill-posed problem (related to the Cauchy problem for an elliptic operator) very few domains admit mother bodies, but for domains with piecewise algebraic boundaries there is a rather constructive and efficient theory, bearing in mind that the same class of domains is also amenable for studying zeros of orthogonal polynomials.

Place, publisher, year, edition, pages
Springer, 2017. p. 77-92
Series
Lecture Notes in Mathematics, ISSN 0075-8434 ; 2199
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-215900DOI: 10.1007/978-3-319-65810-0_6Scopus ID: 2-s2.0-85030684925ISBN: 978-3-319-65809-4 (print)OAI: oai:DiVA.org:kth-215900DiVA, id: diva2:1149796
Note

QC 20171017

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

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  • apa
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