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Hyponormal Quantization of Planar Domains, 2017, Vol.2199, p.93-117
Ort / Verlag
Switzerland: Springer International Publishing AG
Erscheinungsjahr
2017
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
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 1∕1−x2\documentclass[12pt]{minimal}
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$$1/\sqrt{1 - x^{2}}$$
\end{document}, − 1 ≤ x ≤ 1, while the mother body for the ellipse with uniform mass distribution has density 1−x2\documentclass[12pt]{minimal}
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$$\sqrt{ 1 - x^{2}}$$
\end{document} on the same segment.