• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Master's Dissertation
DOI
Document
Author
Full name
Rafael Moreira Neves
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Lopes, Pedro Tavares Paes (President)
Marrocos, Marcus Antonio Mendonça
Siciliano, Gaetano
Title in Portuguese
A Lei de Weyl para o Laplaciano
Keywords in Portuguese
Análise espectral
Núcleo do calor
Semigrupos
Abstract in Portuguese
Demonstramos a Lei de Weyl sobre o comportamento assintótico dos autovalores do operador Laplaciano com condições de contorno de Dirichlet em domínios limitados e suaves com o auxílio do núcleo do calor. Para isso, fazemos um estudo dos operadores não-limitados, semigrupos e da transformada de Fourier. Por fim, expomos alguns resultados posteriores motivados pelo artigo de Mark Kac "Can one hear the shape of a drum?".
Title in English
The Weyl Law for the Laplacian
Keywords in English
Heat kernel
Semigroups
Spectral analysis
Abstract in English
We prove the Weyl Law on the asymptotic behavior of eigenvalues of the Laplace operator with Dirichlet boundary conditions in smooth bounded domains with the help of the heat kernel. To that end, we study unbounded operators, semigroups and the Fourier transform. Lastly, we mention some further results motivated by Mark Kac's article "Can one hear the shape of a drum?".
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
Publishing Date
2019-07-10
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
CeTI-SC/STI
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2020. All rights reserved.