Eigenfunctions of the Laplacian on a Riemannian Manifold (CBMS Regional Conference Series in Mathematics)

Expanded versions of ten lectures delivered at the University of Kentucky in June 2011 introduce the quantum mechanical interpretation of eigenfunctions and their time evolution, the oscillation and concentration of an orthonormal basis of eigenfunctions, and the properties of eigenfunctions of the Laplace operator and of Schrödinger operators. Considerable space is devoted to analytic continuation of eigenfunctions of Laplacians of real analytic Riemannian manifolds to the complexification of the manifold. The rationale for analytic continuation is that the nodal sets are better behaved and easier to study in the complex domain than the real domain. Annotation ©2018 Ringgold, Inc., Portland, OR (protoview.com)