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Quadratic Forms Corresponding to the Generalized Schrödinger Semigroups

✍ Scribed by J Glover; M Rao; H Sikic; R Song

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
527 KB
Volume
125
Category
Article
ISSN
0022-1236

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✦ Synopsis

Suppose that (X_{1}) is the standard Brownian motion in (R^{d}, d \geqslant 3), that (\rho \in H^{1}\left(R^{d}\right)) is a bounded continuous function such that (|\nabla \rho|^{2}) belongs to the Kato class and (\mu) is a measure belonging to the Kato class. Let (A_{t}^{[\rho]}) be defined as (A_{t}^{[p]}=\rho\left(X_{t}\right)-) (\rho\left(X_{0}\right)-\int_{0}^{\prime} \nabla \rho\left(X_{s}\right) \cdot d X_{s}), and let (A_{t}^{\mu}) be the continuous additive functional with (\mu) as its Revuz measure. Define (A), as the sum of the two additive functionals above. Then the semigroup defined as

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