Dirichlet form

In mathematics, a Dirichlet form is a Markovian closed symmetric form on an L²-space.^[1] Such objects are studied in abstract potential theory, based on the classical Dirichlet's principle. The theory of Dirichlet forms originated in the work of Beurling and Deny (1958, 1959) on Dirichlet spaces.

References

1. ^ Fukushima, M, Oshima, Y., & Takeda, M. (1994). Dirichlet forms and symmetric Markov processes. Walter de Gruyter & Co , ISBN 3-11-011626-X

• Beurling, Arne; Deny, J. (1958), "Espaces de Dirichlet. I. Le cas élémentaire", Acta Mathematica 99: 203–224, doi:10.1007/BF02392426, ISSN 0001-5962, MR0098924 
• Beurling, Arne; Deny, J. (1959), "Dirichlet spaces", Proceedings of the National Academy of Sciences of the United States of America 45: 208–215, ISSN 0027-8424, JSTOR 90170, MR0106365 
• Fukushima, Masatoshi (1980), Dirichlet forms and Markov processes, North-Holland Mathematical Library, 23, Amsterdam: North-Holland, ISBN 978-0-444-85421-6, MR569058 
• Jost, Jürgen; Kendall, Wilfrid; Mosco, Umberto; Röckner, Michael; Sturm, Karl-Theodor (1998), New directions in Dirichlet forms, AMS/IP Studies in Advanced Mathematics, 8, Providence, RI: American Mathematical Society, p. xiv+277, ISBN 0-8218-1061-8, MR1652277 .
• Hazewinkel, Michiel, ed. (2001), "Abstract potential theory", Encyclopaedia of Mathematics, Springer, ISBN 978-1556080104, http://eom.springer.de/p/p074150.htm