S. Albeverio, B. K. Driver, M. Gordina, A. M. Vershik, “Equivalence of the Brownian and energy representations”, Zap. Nauchn. Sem. POMI, 2015, Volume 441,Pages <nobr>17

This article is cited in 2 papers

Equivalence of the Brownian and energy representations

S. Albeverio^a, B. K. Driver^b, M. Gordina^c, A. M. Vershik^def

^a Institut für Angewandte Mathematik Abteilung Wahrscheinlichkeitstheorie und HCM Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
^b Department of Mathematics, 0112, University of California, San Diego, La Jolla, CA 92093-0112, U.S.A.
^c Department of Mathematics, University of Connecticut, Storrs, CT 06269, U.S.A.
^d St.Petersburg Department of Steklov Institute of Mathematics, Russian Academy of Sciences, Russia
^e Mathematics and Mechanics Department, St. Petersburg State University, Russia
^f Institue of the Probelm of Transmission of Information, Russia

Abstract: We consider two unitary representations of the infinite-dimensional groups of smooth paths with values in a compact Lie group. The first representation is induced by 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.

Key words and phrases: quasi-invariance, stochastic differential equations, Lie groups, representations of infinite-dimensional groups.

UDC: 519

Received: 19.11.2015

Language: English