Majoration des semi-groupes de contractions de L1 et applications
Majorization of -semigroups in ordered Banach spaces
We give criteria for domination of strongly continuous semigroups in ordered Banach spaces that are not necessarily lattices, and thus obtain generalizations of certain results known in the lattice case. We give applications to semigroups generated by differential operators in function spaces which are not lattices.
Markov operators: applications to diffusion processes and population dynamics
This note contains a survey of recent results concerning asymptotic properties of Markov operators and semigroups. Some biological and physical applications are given.
Markovian bridges and reversible diffusion processes with jumps
Markovian Master Equations. II.
Matrices of operators and regularized semigroups.
Matrix multiplication operators generating one parameter semigroups.
Matrix transformations and generators of analytic semigroups.
Maximal regularity and Hardy spaces
Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in -spaces
Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in -spaces
Several abstract model problems of elliptic and parabolic type with inhomogeneous initial and boundary data are discussed. By means of a variant of the Dore-Venni theorem, real and complex interpolation, and trace theorems, optimal -regularity is shown. By means of this purely operator theoretic approach, classical results on -regularity of the diffusion equation with inhomogeneous Dirichlet or Neumann or Robin condition are recovered. An application to a dynamic boundary value problem with surface...
Maximal regularity for second order non-autonomous Cauchy problems
We consider some non-autonomous second order Cauchy problems of the form ü + B(t)u̇ + A(t)u = f(t ∈ [0,T]), u(0) = u̇(0) = 0. We assume that the first order problem u̇ + B(t)u = f(t ∈ [0,T]), u(0) = 0, has -maximal regularity. Then we establish -maximal regularity of the second order problem in situations when the domains of B(t₁) and A(t₂) always coincide, or when A(t) = κB(t).
Maximal regularity of delay equations in Banach spaces
We characterize existence and uniqueness of solutions for an inhomogeneous abstract delay equation in Hölder spaces. The main tool is the theory of operator-valued Fourier multipliers.
Maximal regularity of discrete and continuous time evolution equations
We consider the maximal regularity problem for the discrete time evolution equation for all n ∈ ℕ₀, u₀ = 0, where T is a bounded operator on a UMD space X. We characterize the discrete maximal regularity of T by two types of conditions: firstly by R-boundedness properties of the discrete time semigroup and of the resolvent R(λ,T), secondly by the maximal regularity of the continuous time evolution equation u’(t) - Au(t) = f(t) for all t > 0, u(0) = 0, where A:= T - I. By recent results of...
Maximizers for the Strichartz Inequality
We compute explicitly the best constants and, by solving some functional equations, we find all maximizers for homogeneous Strichartz estimates for the Schrödinger equation and for the wave equation in the cases when the Lebesgue exponent is an even integer.
Means of vector-valued functions and projections which commute with the action of a group
Measures of finite (r,p)-energy and potentials on a separable metric space
Method of semidiscretization in time for quasilinear integrodifferential equations.
Mild integrated C-existence families
We study mild n times integrated C-existence families without the assumption of exponential boundedness. We present several equivalent conditions for these families. Hille-Yosida type necessary and sufficient conditions are given for the exponentially bounded case.
Mild solutions of quantum stochastic differential equations.