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Laplace operators on differential forms over configuration spaces
 J. Geom. Phys
"... Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on forms and associated semigroups are considered. Their probabilistic interpretation is given. 2000 AMS Mathematics Subject Classification. 60G57, ..."
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Cited by 7 (3 self)
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Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on forms and associated semigroups are considered. Their probabilistic interpretation is given. 2000 AMS Mathematics Subject Classification. 60G57, 58A10Contents
Laplace operators and diffusions in tangent bundles over Poisson spaces
 Preprint SFB 256 No. 629, Universität
, 1999
"... Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on 1forms and associated semigroups are considered. Their probabilistic interpretation is given. 1 ..."
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Cited by 5 (4 self)
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Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on 1forms and associated semigroups are considered. Their probabilistic interpretation is given. 1
de Rham cohomology of configuration spaces with Poisson measure
 J. Funct. Anal
, 1995
"... The space ΓX of all locally finite configurations in a Riemannian manifold X of infinite volume is considered. The deRham complex of squareintegrable differential forms over ΓX, equipped with the Poisson measure, and the corresponding deRham cohomology are studied. The latter is shown to be unitari ..."
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Cited by 4 (0 self)
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The space ΓX of all locally finite configurations in a Riemannian manifold X of infinite volume is considered. The deRham complex of squareintegrable differential forms over ΓX, equipped with the Poisson measure, and the corresponding deRham cohomology are studied. The latter is shown to be unitarily isomorphic to a certain Hilbert tensor algebra generated by the L 2cohomology of the underlying manifold X.
Blowup and stability of semilinear PDE's with gamma generator
, 2004
"... We investigate nitetime blowup and stability of semilinear partial dierential equations of the form @w t =@t = w t +t t , w 0 (x) = '(x) 0, x 2 R+ , where is the generator of the standard gamma process and > 0, 2 R, > 0 are constants. We show that any initial value satisfying c 1 x ..."
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Cited by 1 (1 self)
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We investigate nitetime blowup and stability of semilinear partial dierential equations of the form @w t =@t = w t +t t , w 0 (x) = '(x) 0, x 2 R+ , where is the generator of the standard gamma process and > 0, 2 R, > 0 are constants. We show that any initial value satisfying c 1 x '(x), x > x 0 for some positive constants x 0 ; c 1 ; a 1 , yields a nonglobal solution if a 1 < 1 + , or if a 1 = 1 + and > 1. If '(x) c 2 x , x > x 0 ; where x 0 ; c 2 ; a 2 > 0, and a 2 > 1 + , then the solution w t is global and satis es 0 w t (x) Ct , x 0, for some constant C > 0. This extends the results previously obtained in the case of stable generators. Systems of semilinear PDE's with gamma generators are also considered.