UID:
almahu_9947360001302882
Format:
Online-Ressource (vi, 184 p)
Edition:
Online-Ausg. Palo Alto, Calif ebrary 2011 Electronic reproduction; Available via World Wide Web
ISBN:
311014283X (alk. paper)
,
9783110142839 (alk. paper)
Series Statement:
De Gruyter studies in mathematics 21
Uniform Title:
Veroi-Łatnostnai-Ła teorii-Ła potent-Łsiala na beskonechnomernykh abelevykh gruppakh. ‹engl.›
Content:
Potential Theory On Infinite-Dimensional Abelian Groups (De Gruyter Studies In Mathematics)
Note:
Includes bibliographical references (p. [175]-181) and index
,
3.4 Projective sequences of harmonic spaces: proofs of theorems3.5 Projective sequences of harmonic spaces: some remarks on harmonic functions on a Wiener space; Chapter 4. Markov processes and harmonic structures on a group; 4.1 Harmonic groups; 4.2 Space-homogeneous processes and harmonic functions; 4.3 Space homogeneous processes and harmonic functions: quasidiagonal case; 4.4 Bony's theorem on the group ℝp ×T∞; Chapter 5. Elliptic equations on a group; 5.1 Admissible distributions and multipliers; 5.2 Weak solutions of elliptic equations (Lp-theory).
,
5.3 Weyl's lemma and the hypoelliptic property5.4 Bessel potentials on group T∞; Chapter 6. Special classes of harmonic functions and potentials; 6.1 Spaces Mp⃗ of martingales with mixed norm; 6.2 Classes hp⃗ of harmonic functions in the semispace T∞+; 6.3 Mp⃗ -estimates of potentials. Sobolev inequality on group T∞; Chapter 7. Some thoughts on probability and analysis on locally compact groups; 7.1 Dichotomy problem; 7.2 Harmonic functions on a group; 7.3 The problem of hypoellipticity; 7.4 "Can one hear the shape of a drum?"; 7.5 Geometry on a group; Bibliography; Index.
,
Chapter 1. Introduction; Chapter 2. Elements of potential theory; 2.1 Notation; 2.2 Harmonic and hyperharmonic sheaves; 2.3 The generalized Dirichlet problem; 2.4 Harmonic spaces; 2.5 Brelot and Bauer spaces; 2.6 Smooth Bauer spaces; 2.7 Markov processes; 2.8 Markov processes on harmonic spaces; 2.9 Probability interpretations; 2.10 Duality; Chapter 3. Markov processes and harmonic structures; 3.1 Markov processes and Brelot spaces; 3.2 Markov processes and Bauer spaces; 3.3 Projective sequences of harmonic spaces: examples, definitions, statements of theorems.
Additional Edition:
ISBN 9783110876840
Language:
English
DOI:
10.1515/9783110876840
URL:
http://www.degruyter.com/doi/book/10.1515/9783110876840
