Absorption Semigroups, Feller Property, and Kato Class

Voigt, Jürgen

doi:10.1007/978-3-0348-9092-2_42

Jürgen Voigt⁴

Part of the book series: Operator Theory Advances and Applications ((OT,volume 78))

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Abstract

Let X be a locally compact space, m a measure on the Borel sets of X (satisfying suitable properties), U = (U(t); t ≥ 0) a substochastic (i.e., positive and contractive) strongly continuous semigroup on L ₁(m). Assume further that U*, the adjoint semigroup, satisfies the Feller property, i.e., C _o (X) (continuous functions tending to zero at infinity) is invariant under U*, and U* restricted to C₀(X) is strongly continuous.

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References

W. Arendt, C.J.K. Batty: Absorption semigroups and Dirichlet boundary conditions. Math. Ann. 295, 427–448 (1993).
Article MathSciNet MATH Google Scholar
E. B. Davies: Heat kernels and spectral theory. Cambridge University Press, Cambridge, 1989.
Book MATH Google Scholar
I. MIYADERA: On perturbation theory for semi-groups of operators. Tôhoku Math. J.18, 299–310 (1966).
Article MathSciNet MATH Google Scholar
I. Miyadera: On perturbation for semigroups of linear operators. Scientific Researches, School of Education, Waseda Univ.21, 21–24 (1972) (in Japanese).
Google Scholar
E. M. Ouhabaz: Invariance of closed convex sets and domination criteria for semigroups. Preprint.
Google Scholar
E.-M. Ouhabaz, P. Stollmann, K.-TH. Sturm, J. Voigt: The Feller property for absorption semigroups. Preprint 1994.
Google Scholar
W. Arendt: Gaussian estimates and interpolation of the spectrum in L ^P. Preprint.
Google Scholar
H.H. Schaefer: Topological vector spaces. Springer-Verlag,New York,1971.
Google Scholar
B. Simon: Schrödinger semigroups. Bull. Amer. Math. Soc. (N.S.)7, 447–526 (1982).
Article MathSciNet MATH Google Scholar
P. Stollmann, J. Voigt: Perturbation of Dirichlet forms by measures. Potential Analysis, to appear.
Google Scholar
J. Voigt: On the perturbation theory for strongly continuous semigroups. Math. Ann.229, 163–171 (1977).
Article MathSciNet MATH Google Scholar
J. Voigt: Absorption semigroups, their generators, and Schrödinger semigroups. J. Funct. Anal.67, 167–205 (1986).
Article MathSciNet MATH Google Scholar
J. Voigt: Absorption semigroups. J. Operator Theory20, 117–131 (1988).
MathSciNet MATH Google Scholar

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Fachrichtung Mathematik, Institut für Analysis, Technische Universität Dresden, D-01062, Dresden, Germany
Jürgen Voigt

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Jürgen Voigt
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Institut für Mathematik, Technische Universität Clausthal, Erzstrasse 1, 38678, Clausthal-Zellerfeld, Germany
Michael Demuth
Institut für Mathematik, Max Planck-Arbeitsgruppe “Partielle Differentialgleichungen and Komplexe Analysis” Universität Potsdam, Postfach 60 15 53, 14415, Potsdam, Germany
Bert-Wolfgang Schulze

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Voigt, J. (1995). Absorption Semigroups, Feller Property, and Kato Class. In: Demuth, M., Schulze, BW. (eds) Partial Differential Operators and Mathematical Physics. Operator Theory Advances and Applications, vol 78. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9092-2_42

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DOI: https://doi.org/10.1007/978-3-0348-9092-2_42
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9903-1
Online ISBN: 978-3-0348-9092-2
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