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Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators

Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators

Paperback

Series: Lecture Notes in Mathematics, Book 1718

Medical ReferenceGeneral MathematicsProbability & Statistics

ISBN10: 3540666281
ISBN13: 9783540666288
Publisher: Springer Nature
Published: Nov 17 1999
Pages: 268
Weight: 0.86
Height: 0.58 Width: 6.14 Depth: 9.21
Language: English
This book addresses both probabilists working on diffusion processes and analysts interested in linear parabolic partial differential equations with singular coefficients. The central question discussed is whether a given diffusion operator, i.e., a second order linear differential operator without zeroth order term, which is a priori defined on test functions over some (finite or infinite dimensional) state space only, uniquely determines a strongly continuous semigroup on a corresponding weighted Lp space. Particular emphasis is placed on phenomena causing non-uniqueness, as well as on the relation between different notions of uniqueness appearing in analytic and probabilistic contexts.

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