Eigenvalues and Eigenfunctions of the Laplacian
نویسنده
چکیده
The problem of determining the eigenvalues and eigenvectors for linear operators acting on finite dimensional vector spaces is a problem known to every student of linear algebra. This problem has a wide range of applications and is one of the main tools for dealing with such linear operators. Some of the results concerning these eigenvalues and eigenvectors can be extended to infinite dimensional vector spaces. In this article we will consider the eigenvalue problem for the Laplace operator acting on the L space of functions on a bounded domain in R. We prove that the eigenfunctions form an orthonormal basis for this space of functions and that the eigenvalues of these functions grow without bound.
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تاریخ انتشار 2011