Laplace operators on the cone of Radon measures

Kondratiev Y, Lytvynov E, Vershik A (2015)
Journal of Functional Analysis 269(9): 2947-2976.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Autor/in
Kondratiev, YuriUniBi; Lytvynov, Eugene; Vershik, Anatoly
Abstract / Bemerkung
We consider the infinite-dimensional Lie group (sic) which is the semidirect product of the group of compactly supported diffeomorphisms of a Riemannian manifold X and the commutative multiplicative group of functions on X. The group naturally acts on the space M(X) of Radon measures on X. We would like to define a Laplace operator associated with a natural representation of (sic) in L-2(M(X), mu). Here mu is assumed to be the law of a measure-valued Levy process. A unitary representation of the group cannot be determined, since the measure mu is not qtinsi-invariant with respect to the action of the group (sic). Consequently, operators of a representation of the Lie algebra and its universal enveloping algebra (in particular, a Laplace operator) are not defined. Nevertheless, we determine the Laplace operator by using a special property of the action of the group (sic) (a partial quasi-invariance). We further prove the essential self-adjointness of the Laplace operator. Finally, we explicitly construct a diffusion process on M(X) whose generator is the Laplace operator. (C) 2015 Elsevier Inc. All rights reserved.
Stichworte
Completely random measure; Diffusion process; Representations of big groups; Laplace operator
Erscheinungsjahr
2015
Zeitschriftentitel
Journal of Functional Analysis
Band
269
Ausgabe
9
Seite(n)
2947-2976
ISSN
0022-1236
Page URI
https://pub.uni-bielefeld.de/record/2782598

Zitieren

Kondratiev Y, Lytvynov E, Vershik A. Laplace operators on the cone of Radon measures. Journal of Functional Analysis. 2015;269(9):2947-2976.
Kondratiev, Y., Lytvynov, E., & Vershik, A. (2015). Laplace operators on the cone of Radon measures. Journal of Functional Analysis, 269(9), 2947-2976. doi:10.1016/j.jfa.2015.06.007
Kondratiev, Y., Lytvynov, E., and Vershik, A. (2015). Laplace operators on the cone of Radon measures. Journal of Functional Analysis 269, 2947-2976.
Kondratiev, Y., Lytvynov, E., & Vershik, A., 2015. Laplace operators on the cone of Radon measures. Journal of Functional Analysis, 269(9), p 2947-2976.
Y. Kondratiev, E. Lytvynov, and A. Vershik, “Laplace operators on the cone of Radon measures”, Journal of Functional Analysis, vol. 269, 2015, pp. 2947-2976.
Kondratiev, Y., Lytvynov, E., Vershik, A.: Laplace operators on the cone of Radon measures. Journal of Functional Analysis. 269, 2947-2976 (2015).
Kondratiev, Yuri, Lytvynov, Eugene, and Vershik, Anatoly. “Laplace operators on the cone of Radon measures”. Journal of Functional Analysis 269.9 (2015): 2947-2976.