Introduction to Dirichlet forms

Koordinaten:
Dienstag, 19:00-20:30 in 41/238

Inhalt:
0. Instead of an introduction
1. Functional analytic basics
  1.1 Closed and self adjoint operators
  1.2 Closed forms
  1.3 Generalized derivatives and the classical Dirichlet form
  1.4 The spectral theorem
  1.5 Positive forms, operators semigroups, resolvents and back
2. Dirichlet forms
  2.1 The Beurling Deny criteria
  2.2 More examples
  2.3 Regular Dirichlet forms and capacity
  2.4 Measures of finite energy integral

Bouleau, N. and Hirsch, F.
Dirichlet forms and analysis on Wiener space.
de Gruyter Studies in Mathematics, 14.
Walter de Gruyter & Co., Berlin, 1991. x+325 pp. ISBN 3-11-012919-1

E.B. Davies
Heat kernels and spectral theory
Cambridge tracts in Mathematics
Cambridge University Press, Cambridge 1989

Fukushima, M.
Dirichlet forms and Markov processes.
North-Holland Mathematical Library, 23.
North-Holland Publishing Co., Amsterdam-New York; Kodansha, Ltd., Tokyo,
1980. x+196 pp. ISBN 0-444-85421-5

Fukushima, M., Oshima, Y and Takeda, M.
Dirichlet forms and symmetric Markov processes.
de Gruyter Studies in Mathematics, 19.
Walter de Gruyter & Co., Berlin, 1994. x+392 pp. ISBN 3-11-011626-X

Ma, Zhi Ming and Röckner, M.
Introduction to the theory of (nonsymmetric) Dirichlet forms.
Universitext.
Springer-Verlag, Berlin, 1992. vi+209 pp. ISBN 3-540-55848-9