Potential Theory on Locally Compact Abelian Groups

Classical potential theory can be roughly characterized as the study of Newtonian potentials and the Laplace operator on the Euclidean space JR3. It was discovered around 1930 that there is a profound connection between classical potential 3 theory and the theory of Brownian motion in JR . The Brown...

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Main Authors: van den Berg, C., Forst, G. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1975, 1975
Edition:1st ed. 1975
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I. Harmonic Analysis
  • § 1. Notation and Preliminaries
  • § 2. Some Basic Results From Harmonic Analysis
  • § 3. Positive Definite Functions
  • § 4. Fourier Transformation of Positive Definite Measures
  • § 5. Positive Definite Functions on ?
  • § 6. Periodicity
  • II. Negative Definite Functions and Semigroups
  • § 7. Negative Definite Functions
  • § 8. Convolution Semigroups
  • § 9. Completely Monotone Functions and Bernstein Functions
  • § 10. Examples of Negative Definite Functions and Convolution Semigroups
  • § 11. Contraction Semigroups
  • § 12. Translation Invariant Contraction Semigroups
  • III. Potential Theory for Transient Convolution Semigroups
  • § 13. Transient Convolution Semigroups
  • § 14. Transient Convolution Semigroups on the Half-Axis and Integrals of Convolution Semigroups
  • § 15. Convergence Lemmas and Potential Theoretic Principles
  • § 16. Excessive Measures
  • § 17. Fundamental Families Associated With Potential Kernels
  • § 18. The Lé