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Fundamental solutions and eigenfunction expansions for Schrödinger operators I. Fundamental solutions

✍ Scribed by Hitoshi Kitada


Publisher
Springer-Verlag
Year
1988
Tongue
French
Weight
440 KB
Volume
198
Category
Article
ISSN
0025-5874

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On Fundamental Solutions of Generalized
✍ Zhongwei Shen 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 268 KB

We consider the generalized Schro dinger operator &2++, where + is a nonnegative Radon measure in R n , n 3. Assuming that + satisfies certain scale-invariant Kato conditions and doubling conditions we establish the following bounds for the fundamental solution of &2++ in R n , where d(x, y, +) is

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## Abstract We study in detail Schrödinger–type operators on a bounded interval of **R** with dissipative boundary conditions. The characteristic function of this operator is computed, its minimal self–adjoint dilation is constructed and the generalized eigenfunction expansion for the dilation is d