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
Conditional Gaugeability and Subcriticality of Generalized Schrödinger Operators
✍ Scribed by Masayoshi Takeda
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 222 KB
- Volume
- 191
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
We obtain a necessary and sufficient condition for conditional gaugeability and show the equivalence between conditional gaugeability and subcriticality of generalized Schrödinger type operators. We apply the condition to concrete examples.
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We investigate the Schro dinger operator H=&2+V acting in L 2 (R n ), n 2, for potentials V that satisfy : x V(x)=O(|x| &|:| ) as |x| Ä . By introducing coordinates on R n closely related to a relevant eikonal equation we obtain an eigenfunction expansion for H at high energies.
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