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In this review we describe the basic structure of positive continuous one-parameter semigroups acting on ordered Banach spaces. The review is in two parts.
In this paper we survey the Perron-Frobenius spectral theory for positive semigroups on Banach lattices and indicate its applications to stability theory of retarded differential equations and quasi-periodic flows.
We present methods using positive semigroups and perturbation theory in the application to the linear Boltzmann equation. Besides being a review, this paper also presents generalizations of known results and develops known methods in a more abstract setting.
A survey of the recent work on the infinitesimal generators of one-parameter semigroups of positivity preserving maps on operator algebras, in the presence of compact symmetry groups or flows.
For an arbitrary uniformly continuous completely positive semigroup (ℱ
:t⩾0) on the space[Figure not available: see fulltext.] of bounded operators on a Hilbert space[Figure not available: see fulltext.], we construct a family (U(t)∶t≥0) of unitary operators on a Hilbert space[Figure not...
Methods of constructing semigroups of operators describing interacting particle systems are reviewed. A simple proof is given showing the existence of semigroups of operators on the space of bounded Borel measurable functions for nonnegative continuous attractive spin rates along with a proof of...
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