Отправить статью по E-mail Equivalence of the Brownian and Energy Representations
- Авторы: Albeverio S.1, Driver B.K.2, Gordina M.3, Vershik A.M.4
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Учреждения:
- Rheinische Friedrich-Wilhelms-Universit¨at
- University of California
- University of Connecticut
- St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg State University, Institute of Problems of Transmission of Information
- Выпуск: Том 219, № 5 (2016)
- Страницы: 612-630
- Раздел: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/238641
- DOI: https://doi.org/10.1007/s10958-016-3134-1
- ID: 238641
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Аннотация
We consider two unitary representations of infinite-dimensional groups of smooth paths with values in a compact Lie group. The first representation is induced by the quasi-invariance of the Wiener measure, and the second representation is the energy representation. We define these representations and their basic properties, and then we prove that these representations are unitarily equivalent. Bibliography: 28 titles.
Об авторах
S. Albeverio
Rheinische Friedrich-Wilhelms-Universit¨at
Автор, ответственный за переписку.
Email: albeverio@iam.uni-bonn.de
Германия, Bonn
B. Driver
University of California
Email: albeverio@iam.uni-bonn.de
США, La Jolla, San Diego
M. Gordina
University of Connecticut
Email: albeverio@iam.uni-bonn.de
США, Storrs
A. Vershik
St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg State University, Institute of Problems of Transmission of Information
Email: albeverio@iam.uni-bonn.de
Россия, St.Petersburg
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