｛\mathbb｛S｝｝^2上Schrödinger本征函数的局部（L^p\）范数

IF 0.5 Q3 MATHEMATICS Annales Mathematiques du Quebec Pub Date : 2021-06-10 DOI:10.1007/s40316-021-00167-5

Gabriel Rivière

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引用次数: 0

摘要

在正则2-球面上，对于Schrödinger本征函数，我们获得了一个关于势的简单几何准则，在该准则下，我们可以在给定点附近，并且对于每一个\（p\ne 6\），通过本征值的幂来改进Sogge估计。该准则可以用势的Radon变换的临界点来表示，并且与本征函数的选择无关。

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Local \(L^p\) norms of Schrödinger eigenfunctions on \({\mathbb {S}}^2\)

On the canonical 2-sphere and for Schrödinger eigenfunctions, we obtain a simple geometric criterion on the potential under which we can improve, near a given point and for every \(p\ne 6\), Sogge’s estimates by a power of the eigenvalue. This criterion can be formulated in terms of the critical points of the Radon transform of the potential and it is independent of the choice of eigenfunctions.

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Annales Mathematiques du Quebec MATHEMATICS-

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1.10

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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.

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