Perturbation of translation invariant positivity preserving semigroups on $L^{2}(\textbf {R}^{N})$
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- by Ira W. Herbst and Alan D. Sloan
- Trans. Amer. Math. Soc. 236 (1978), 325-360
- DOI: https://doi.org/10.1090/S0002-9947-1978-0470750-2
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Abstract:
The theory of singular local perturbations of translation invariant positivity preserving semigroups on ${L^2}({{\mathbf {R}}^N},{d^N}x)$ is developed. A powerful approximation theorem is proved which allows the treatment of a very general class of singular perturbations. Estimates on the local singularities of the kernels of the semigroups, ${e^{ - tH}}$, are given. Eigenfunction expansions are derived. The local singularities of the eigenfunction and generalized eigenfunctions are discussed. Results are illustrated with examples involving singular perturbations of —$\Delta$.References
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Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 236 (1978), 325-360
- MSC: Primary 47D05; Secondary 35P99, 81.47
- DOI: https://doi.org/10.1090/S0002-9947-1978-0470750-2
- MathSciNet review: 0470750