Scattering by Obstacles of Finite Capacity

✍ Scribed by P. Stollmann

• Book ID: 102592706
• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 318 KB
• Volume: 121
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1994.1054

✦ Synopsis

For very general generators of diffusion semigroups we show that the essential and absolutely continuous spectra do not change when one adds an extra Dirichlet boundary condition on a "small" set. This is done by proving that the corresponding semigroup differences are Hilbert-Schmidt or trace class, respectively. Our method consists in a factorization argument which is based on calculating the semigroup difference via the Feynman-Kac formula. We also derive trace class estimates for differences of resolvent powers, provided the underlying semigroup has finite local dimension. 1994 Academic Press, Inc.