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Catalogue Information
Field name	Details
Dewey Class	519.2
Title	Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators ([EBook] /) / by Andreas Eberle.
Author	Eberle, Andreas
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1999.
Physical Details	VIII, 268 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1718
ISBN	9783540480761
Summary Note	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.:
Contents note	Motivation and basic definitions: Uniqueness problems in various contexts -- L p uniqueness in finite dimensions -- Markov uniqueness -- Probabilistic aspects of L p and Markov uniqueness -- First steps in infinite dimensions.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0103045
Links to Related Works	Subject References: Group theory . Group Theory and Generalizations . Mathematics . Partial differential equations . Potential Theory . Potential theory (Mathematics) . Probabilities . Probability theory and stochastic processes . Authors: Eberle, Andreas . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 519.2 .

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

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