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On Evgrafov-Fedoryuk's theory and quadratic differentials
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 1
2015 (English)In: Analysis and Mathematical Physics, ISSN 1664-2368, E-ISSN 1664-235X, Vol. 5, no 2, 171-181 p.Article in journal (Refereed) Published
Abstract [en]

The purpose of this note is to recall the theory of the (homogenized) spectral problem for Schrodinger equation with a polynomial potential and its relation with quadratic differentials. We derive from results of this theory that the accumulation rays of the eigenvalues of the latter problem are in -correspondence with the short geodesics of the singular planar metrics induced by the corresponding quadratic differential. We prove that for a polynomial potential of degree the number of such accumulation rays can be any positive integer between (d - 1) and (d/2) .

Place, publisher, year, edition, pages
2015. Vol. 5, no 2, 171-181 p.
Keyword [en]
Spectral asymptotics, Quadratic differentials, Singular planar metric, Geodesics
National Category
URN: urn:nbn:se:su:diva-117760DOI: 10.1007/s13324-014-0092-yISI: 000354133500004OAI: diva2:819657
Available from: 2015-06-11 Created: 2015-06-01 Last updated: 2015-06-11Bibliographically approved

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Shapiro, Boris
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