Dirichlet Forms Constructed from Annihilation Operators on Bernoulli Functionals
The annihilation operators on Bernoulli functionals (Bernoulli annihilators, for short) and their adjoint operators satisfy a canonical anticommutation relation (CAR) in equal-time. As a mathematical structure, Dirichlet forms play an important role in many fields in mathematical physics. In this pa...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/8278161 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562888085078016 |
|---|---|
| author | Caishi Wang Beiping Wang |
| author_facet | Caishi Wang Beiping Wang |
| author_sort | Caishi Wang |
| collection | DOAJ |
| description | The annihilation operators on Bernoulli functionals (Bernoulli annihilators, for short) and their adjoint operators satisfy a canonical anticommutation relation (CAR) in equal-time. As a mathematical structure, Dirichlet forms play an important role in many fields in mathematical physics. In this paper, we apply the Bernoulli annihilators to constructing Dirichlet forms on Bernoulli functionals. Let w be a nonnegative function on N. By using the Bernoulli annihilators, we first define in a dense subspace of L2-space of Bernoulli functionals a positive, symmetric, bilinear form Ew associated with w. And then we prove that Ew is closed and has the contraction property; hence, it is a Dirichlet form. Finally, we consider an interesting semigroup of operators associated with w on L2-space of Bernoulli functionals, which we call the w-Ornstein-Uhlenbeck semigroup, and, by using the Dirichlet form, Ew we show that the w-Ornstein-Uhlenbeck semigroup is a Markov semigroup. |
| format | Article |
| id | doaj-art-8761dc39e0294181b9dbca8010b08587 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-8761dc39e0294181b9dbca8010b085872025-02-03T01:21:34ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/82781618278161Dirichlet Forms Constructed from Annihilation Operators on Bernoulli FunctionalsCaishi Wang0Beiping Wang1School of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaSchool of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaThe annihilation operators on Bernoulli functionals (Bernoulli annihilators, for short) and their adjoint operators satisfy a canonical anticommutation relation (CAR) in equal-time. As a mathematical structure, Dirichlet forms play an important role in many fields in mathematical physics. In this paper, we apply the Bernoulli annihilators to constructing Dirichlet forms on Bernoulli functionals. Let w be a nonnegative function on N. By using the Bernoulli annihilators, we first define in a dense subspace of L2-space of Bernoulli functionals a positive, symmetric, bilinear form Ew associated with w. And then we prove that Ew is closed and has the contraction property; hence, it is a Dirichlet form. Finally, we consider an interesting semigroup of operators associated with w on L2-space of Bernoulli functionals, which we call the w-Ornstein-Uhlenbeck semigroup, and, by using the Dirichlet form, Ew we show that the w-Ornstein-Uhlenbeck semigroup is a Markov semigroup.http://dx.doi.org/10.1155/2017/8278161 |
| spellingShingle | Caishi Wang Beiping Wang Dirichlet Forms Constructed from Annihilation Operators on Bernoulli Functionals Advances in Mathematical Physics |
| title | Dirichlet Forms Constructed from Annihilation Operators on Bernoulli Functionals |
| title_full | Dirichlet Forms Constructed from Annihilation Operators on Bernoulli Functionals |
| title_fullStr | Dirichlet Forms Constructed from Annihilation Operators on Bernoulli Functionals |
| title_full_unstemmed | Dirichlet Forms Constructed from Annihilation Operators on Bernoulli Functionals |
| title_short | Dirichlet Forms Constructed from Annihilation Operators on Bernoulli Functionals |
| title_sort | dirichlet forms constructed from annihilation operators on bernoulli functionals |
| url | http://dx.doi.org/10.1155/2017/8278161 |
| work_keys_str_mv | AT caishiwang dirichletformsconstructedfromannihilationoperatorsonbernoullifunctionals AT beipingwang dirichletformsconstructedfromannihilationoperatorsonbernoullifunctionals |