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ファイル | 記述 | サイズ | フォーマット | |
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B65-08.pdf | 4.53 MB | Adobe PDF | 見る/開く |
タイトル: | Localized $L^{p}$-estimates for eigenfunctions: II (Harmonic Analysis and Nonlinear Partial Differential Equations) |
著者: | Sogge, Christopher D. |
キーワード: | 58J51 35P15 35R01 42B37 Eigenfunctions localization quantum ergodicity |
発行日: | May-2017 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
誌名: | 数理解析研究所講究録別冊 |
巻: | B65 |
開始ページ: | 141 |
終了ページ: | 152 |
抄録: | If (M; g) is a compact Riemannian manifold of dimension n ≥ 2 we give necessary and sufficient conditions for improved Lp(M)-norms of eigenfunctions for all 2 < p ≠ pc = 2(n+1)/n-1, the critical exponent. Since improved Lpc (M) bounds imply improvement all other exponents, these conditions are necessary for improved bounds for the critical space. We also show that improved Lpc (M) bounds are valid if these conditions are met and if the half-wave operators, U(t), have no caustics when t ≠ 0. The problem of finding a necessary and sufficient condition for Lpc (M) improvement remains an interesting open problem. |
記述: | "Harmonic Analysis and Nonlinear Partial Differential Equations". July 4~6, 2016. edited by Hideo Kubo and Hideo Takaoka. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. |
著作権等: | © 2017 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. |
URI: | http://hdl.handle.net/2433/243685 |
出現コレクション: | B65 Harmonic Analysis and Nonlinear Partial Differential Equations |
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