单位圆盘上拉普拉斯本征函数的增长率

IF 0.5 Q3 MATHEMATICS

Annales Mathematiques du Quebec Pub Date : 2023-08-03 DOI:10.1007/s40316-023-00219-y

Guillaume Lavoie, Guillaume Poliquin

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引用次数: 0

摘要

我们描述了单位圆盘上具有迪里夏特和诺伊曼边界条件的 \(L^2\)-normalized Laplace 特征函数的增长率。特别是，我们证明了狄利克特和诺伊曼特征函数的增长率都是有界的，远离零。我们的方法始于 P. Sarnak 增长指数，并使用了贝塞尔函数或其零点的几个关键渐近公式。

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Growth rates of Laplace eigenfunctions on the unit disk

We give a description of the growth rates of \(L^2\)-normalized Laplace eigenfunctions on the unit disk with Dirichlet and Neumann boundary conditions. In particular, we show that the growth rates of both Dirichlet and Neumann eigenfunctions are bounded away from zero. Our approach starts with P. Sarnak growth exponents and uses several key asymptotic formulas for Bessel functions or their zeros.

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来源期刊

Annales Mathematiques du Quebec MATHEMATICS-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： The goal of the Annales mathématiques du Québec (formerly: Annales des sciences mathématiques du Québec) is to be a high level journal publishing articles in all areas of pure mathematics, and sometimes in related fields such as applied mathematics, mathematical physics and computer science. Papers written in French or English may be submitted to one of the editors, and each published paper will appear with a short abstract in both languages. History: The journal was founded in 1977 as „Annales des sciences mathématiques du Québec”, in 2013 it became a Springer journal under the name of “Annales mathématiques du Québec”. From 1977 to 2018, the editors-in-chief have respectively been S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea. Les Annales mathématiques du Québec (anciennement, les Annales des sciences mathématiques du Québec) se veulent un journal de haut calibre publiant des travaux dans toutes les sphères des mathématiques pures, et parfois dans des domaines connexes tels les mathématiques appliquées, la physique mathématique et l''informatique. On peut soumettre ses articles en français ou en anglais à l''éditeur de son choix, et les articles acceptés seront publiés avec un résumé court dans les deux langues. Histoire: La revue québécoise “Annales des sciences mathématiques du Québec” était fondée en 1977 et est devenue en 2013 une revue de Springer sous le nom Annales mathématiques du Québec. De 1977 à 2018, les éditeurs en chef ont respectivement été S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea.