An approach to spectral problems on Riemannian manifolds
Copyright policy )An approach to spectral problems on Riemannian manifolds
It is shown that eigenvalues of Laplace-Beltrami operators on compact Riemannian manifolds can be determined as limits of eigenvalues of certain finite-dimensional operators in spaces of polyharmonic functions with singularities. In particular, a bounded set of eigenvalues can be determined using a space of such polyharmonic functions with a fixed set of singularities. It also shown that corresponding eigenfunctions can be reconstructed as uniform limits of the same polyharmonic functions with appropriate fixed set of singularities.
Published in Pacific J. Math. 215 (2004), no. 1, 183-199
Mathematics - Functional Analysis, polyharmonic function, Potential theory on Riemannian manifolds and other spaces, Laplace-Beltrami operator, Spectral problems; spectral geometry; scattering theory on manifolds, eigenvalues, FOS: Mathematics, General topics in linear spectral theory for PDEs, Biharmonic and polyharmonic equations and functions in higher dimensions, Functional Analysis (math.FA)
Mathematics - Functional Analysis, polyharmonic function, Potential theory on Riemannian manifolds and other spaces, Laplace-Beltrami operator, Spectral problems; spectral geometry; scattering theory on manifolds, eigenvalues, FOS: Mathematics, General topics in linear spectral theory for PDEs, Biharmonic and polyharmonic equations and functions in higher dimensions, Functional Analysis (math.FA)
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