Asymptotic Behavior of Spectrums for Elliptic Pseudo-differential Operators
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Date
2015-03-17
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Johns Hopkins University
Abstract
The aim of this dissertation is to study the asymptotic behaviors of spectrums for Elliptic Pseudo-seudodifferential Operators. In this work we included two results. First we studied the Nodal set of Steklov Eigenfunctions and obtained a lower bound for its size. Then we refined an end pioint estimate of Laplace-Beltrami eigenfunctions restricted to totally geodesic submanifolds.
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Keywords
Spectrum, Eigenfunction, Nodal Sets, Restriction to Submanifolds