For the eigenvalues . n / 1 nD1 of the Dirichlet Laplacian on a bounded convex domain C, we find the sum of the series the regularized trace of the inverse of Dirichlet Laplacian.
On traces associated with the Dirichlet Laplacian
β Scribed by M van den Berg
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 311 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0022-247X
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## Abstract For an arbitrary differential operator __P__ of order __p__ on an open set __X__ β R^n^, the Laplacian is defined by Ξ = __P__\*__P__. It is an elliptic differential operator of order __2p__ provided the symbol mapping of __P__ is injective. Let __O__ be a relatively compact domain in _
In 1953 Minakshisundarum [6] published a new and simpler proofbased on the heat equation-of results concerning the characteristic functions and values of the Laplace-Beltrami operator on a closed Riemannian manifold which he had obtained earlier in collaboration with Pleijel. Shortly afterward Prof