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Lp-Uniqueness of Schrödinger Operators and the Capacitary Positive Improving Property

✍ Scribed by Liming Wu

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
237 KB
Volume
182
Category
Article
ISSN
0022-1236

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✦ Synopsis

We prove several L p -uniqueness results for Schro dinger operators &L+V by means of the Feynman Kac formula. Using the (m, p)-capacity theory for general Markov semigroups, we show that the associated Feynman Kac semigroup is positive improving in the sense of (m, p)-capacity, improving the well known one in the sense of measure. Using that capacitary positive improving property and two new inequalities for generalized Ornstein Uhlenbeck generators, we show the essential self-adjointness of the ground state diffusion generator L , =L+21(,, } )Â, associated with two dimensional Euclidean quantum fields.

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