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Lookup NU author(s): Professor Mihai Putinar


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© Springer International Publishing AG 2017. In this chapter we present the results of our numerical experiments concerning zeros of exponential polynomials, with pictures indicating asymptotic distributions (or, at least, the distribution of the first 50–100 zeros). We also make the corresponding theoretical construction of mother bodies, and compare the two. In many cases there are reasonable, but far from perfect, agreements between the sets where zeros seem to accumulate and the supports of the corresponding mother bodies. And here we reach terra incognito as there is no agreement between the densities: they seem rather to be complementary to each other. In one case we have complete results, with theoretical proofs, namely for the ellipse. Taking a standard ellipse with foci ± 1, the zeros go to the focal segment, with density proportional to (Forumala prsented).while the mother body for the ellipse with uniform mass distribution has density (Forumala prsented). on the same segment.

Publication metadata

Author(s): Gustafsson B, Putinar M

Publication type: Book Chapter

Publication status: Published

Book Title: Hyponormal Quantization of Planar Domains: Exponential Transform in Dimension Two

Year: 2017

Volume: 2199

Pages: 93-117

Online publication date: 26/09/2017

Acceptance date: 02/04/2016

Series Title: Lecture Notes in Mathematics

Publisher: Springer Verlag

Place Published: Cham, Switzerland


DOI: 10.1007/978-3-319-65810-0_7

Library holdings: Search Newcastle University Library for this item

ISBN: 9783319658094