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  • Book
  • © 1999

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

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1718)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-VIII
  2. Introduction

    • Andreas Eberle
    Pages 1-8
  3. L p uniqueness in finite dimensions

    • Andreas Eberle
    Pages 41-87
  4. Markov uniqueness

    • Andreas Eberle
    Pages 89-167
  5. First steps in infinite dimensions

    • Andreas Eberle
    Pages 185-253
  6. Back Matter

    Pages 255-260

About this book

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.

Keywords

  • Differential operator
  • differential equation
  • diffusion process
  • essentially self-adjoint
  • generator
  • partial differential equation
  • semigroup
  • uniqueness
  • partial differential equations

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions