Non-Differentiability of Heat Semigroups in Infinite Dimensional Hilbert Spaces

Guiotto, Paolo

doi:10.1007/pl00005925

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Laplace Operators On Abstract Wiener Spaces1

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Cited by 5 publications

(2 citation statements)

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“…Remark 3.15. A similar result is obtained [5] in the settings of heat semigroups in Hilbert spaces (see e.g. [13]).…”

Section: Laplace Operators On Abstract Wiener Spacessupporting

confidence: 81%

Generators of Brownian motions on abstract Wiener spaces

Harada

2010

Noncommutative Harmonic Analysis With Applications to Probability II

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“…Remark 3.15. A similar result is obtained [5] in the settings of heat semigroups in Hilbert spaces (see e.g. [13]).…”

Section: Laplace Operators On Abstract Wiener Spacessupporting

confidence: 81%

Generators of Brownian motions on abstract Wiener spaces

Harada

2010

Noncommutative Harmonic Analysis With Applications to Probability II

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“…Using the characterization of the generator of P t t^0 given in [2], Theorem 4.1, Guiotto [7] recently proved the non-differentiability of P t t^0 on UBC H.…”

mentioning

confidence: 99%

On the norm continuity of transition semigroups in Hilbert spaces

Desch

Rhandi

1998

Archiv der Mathematik

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The solution semigroup for certain anisotropic heat equations on an infinite dimensional Hilbert space can be defined, e.g., by a limit of finite dimensional Gaussian semigroups. Unlike the heat equation in a finite dimensional Euclidean space, the solution semigroup is known not to be differentiable (and, a fortiori, not analytic). The present paper improves this result and shows that the semigroup is in fact not norm continuous at any time. The proof is performed by elementary computations.

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