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  3. Positive Harmonic Functions and Diffusion
  • Cited by 185
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    • Publisher:
      Cambridge University Press
      Publication date:
      December 2009
      January 1995
      ISBN:
      9780511526244
      9780521470148
      9780521059831
      DOI:
      https://doi.org/10.1017/CBO9780511526244
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.879kg, 492 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.773kg, 492 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
      Series:
      Cambridge Studies in Advanced Mathematics (45)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
    Series:
    Cambridge Studies in Advanced Mathematics (45)
    Information

    Book description

    In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.

    Reviews

    Review of the hardback:‘This book is reasonably self contained, accessible even to a graduate student but maintaining a high level of mathematical rigor.’

    Source: European Mathematical Society Newsletter

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