SECOND QUANTIZATION AND THE Lp-SPECTRUM OF NONSYMMETRIC ORNSTEIN–UHLENBECK OPERATORS

DOI10.1142/S0219025705002074zbMath1089.35083arXivmath-ph/0509057MaRDI QIDQ5708783

J. M. A. M. van Neerven

Publication date: 21 November 2005

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0509057

zbMATH Keywords

Wiener processstrongly continuous semigroupcontraction semigroupstrong Feller propertysymmetric Fock spaceinfinite dimensional Langevin equationMetafune-Pallara-Priola formula

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Markov semigroups and applications to diffusion processes (47D07) Groups and semigroups of linear operators (47D03) Geometry and quantization, symplectic methods (81S10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15)

Related Items (7)

\(L^{1}\)-spectrum of Banach space valued Ornstein--Uhlenbeck operators ⋮ Spectral analysis of localized rotating waves in parabolic systems ⋮ Lévy-Ornstein-Uhlenbeck transition semigroup as second quantized operator ⋮ On the eigenfunctions of the complex Ornstein-Uhlenbeck operators ⋮ Ornstein–Uhlenbeck operators and semigroups ⋮ ON THE DOMAIN OF NONSYMMETRIC ORNSTEIN–UHLENBECK OPERATORS IN BANACH SPACES ⋮ Riesz transforms for a non-symmetric Ornstein--Uhlenbeck semigroup

Cites Work

• The spectrum of a Schrödinger operator in \(L_ p({\mathbb{R}}^{\nu})\) is p-independent
• Nonsymmetric Ornstein-Uhlenbeck semigroups in Banach spaces
• Spectral properties of hypoelliptic operators
• Transition semigroups of Banach space-valued Ornstein-Uhlenbeck processes
• Spectrum of Ornstein-Uhlenbeck operators in \(L ^{p}\) spaces with respect to invariant measures
• Existence, uniqueness and invariant measures for stochastic semilinear equations on Hilbert spaces
• Fourier's law for a harmonic crystal with self-consistent stochastic reservoirs
• On the spectra of operators on tensor products
• Tensor products of closed operators on Banach spaces
• On uniqueness of invariant measures for finite- and infinite-dimensional diffusions
• Ergodicity for Infinite Dimensional Systems
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