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Mother Bodies

Lookup NU author(s): Professor Mihai Putinar


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© Springer International Publishing AG 2017. 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.

Publication metadata

Author(s): Gustafsson B, Putinar M

Editor(s): Gustafsson B; Putinar M

Publication type: Book Chapter

Publication status: Published

Book Title: Hyponormal Quantization of Planar Domains

Year: 2017

Volume: 2199

Pages: 77-92

Print publication date: 18/10/2017

Online publication date: 26/09/2017

Acceptance date: 02/04/2016

Series Title: Lecture Notes in Mathematics

Publisher: Springer Verlag

Place Published: Cham


DOI: 10.1007/978-3-319-65810-0_6

Library holdings: Search Newcastle University Library for this item

ISBN: 9783319658094