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Graduate Seminar
Giovanni Gravina Carnegie Mellon University Title: Eigenvalues and eigenfunctions of the Laplacian Abstract: The Dirichlet eigenvalues are the fundamental modes of vibration of an idealized drum with a given shape. In this talk we will study the associated eigenvalue problem by means of constrained optimization. The main result we'll discuss is the spectral theorem for the Dirichlet Laplacian. This can be stated as follows: the eigenfunctions of the Dirichlet Laplacian form an orthonormal basis for the space of squareintegrable functions on a bounded domain. Date: Tuesday, April 18, 2017 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Yangxi Ou Note: Video on Youtube: https://youtu.be/bfUD8Ea0vU 