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Conditional Gauge and Potential Theory for the Schrödinger Operator

✍ Scribed by M. Cranston, E. Fabes and Z. Zhao


Book ID
125691114
Publisher
American Mathematical Society
Year
1988
Tongue
English
Weight
495 KB
Volume
307
Category
Article
ISSN
0002-9947

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Consider the Schr6dinger operator H= (A/2)+ q in a bounded C 1,~ domain D with q e K~ °c. (D, q) satisfies the condition: sup[spec((A/2) + q)lD] < 0. Let V and G denote the Green functions in D for H and L1/2, respectively. We prove that where (xr) is the conditioned Brownian motion starting at x a

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## Abstract The absolutely continuous and singular spectrum of one‐dimensional Schrödinger operators with slowly oscillating potentials and perturbed periodic potentials is studied, continuing similar investigations for Jacobi matrices from [14]. Trace class methods are used to locate the singular