Semigroup formulation and approximation of a linear age-dependent population problem with spatial diffusion.
Semi-groupes sous-Markoviens engendrés par des opérateurs matriciels.
Semigroups affiliated with algebras of operators
Semigroups and resolvents of bounded variation, imaginary powers and H°° functional calculus.
Semigroups with nonquasianalytic growth
We study asymptotic behavior of -semigroups T(t), t ≥ 0, such that ∥T(t)∥ ≤ α(t), where α(t) is a nonquasianalytic weight function. In particular, we show that if σ(A) ∩ iℝ is countable and Pσ(A*) ∩ iℝ is empty, then , ∀x ∈ X. If, moreover, f is a function in which is of spectral synthesis in a corresponding algebra with respect to (iσ(A)) ∩ ℝ, then , where . Analogous results are obtained also for iterates of a single operator. The results are extensions of earlier results of Katznelson-Tzafriri,...
Semilinear Cauchy Problems with Almost Sectorial Operators
Existence of a mild solution to a semilinear Cauchy problem with an almost sectorial operator is studied. Under additional regularity assumptions on the nonlinearity and initial data we also prove the existence of a classical solution to this problem. An example of a parabolic problem in Hölder spaces illustrates the abstract result.
Semilinear evolution equations of the parabolic type
This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.
Semilinear integro-differential equations with compact semigroups.
Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator
The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information on the...
Sharp estimates for the Ornstein-Uhlenbeck operator
Let be the Ornstein-Uhlenbeck operator which is self-adjoint with respect to the Gauss measure on We prove a sharp estimate of the operator norm of the imaginary powers of on
Shilov parabolic systems
Short-time heat flow and functions of bounded variation in
We prove a characterisation of sets with finite perimeter and functions in terms of the short time behaviour of the heat semigroup in . For sets with smooth boundary a more precise result is shown.
Singular evolution problems, regularization, and applications to physics, engineering, and biology
Slowly changing vectors and the asymptotic finite-dimensionality of an operator semigroup.
Smoothing effect for Schrödinger evolution equation via commutator algebra
Solution semigroup and invariant manifolds for functional equations with infinite delay
It is proved that parabolic equations with infinite delay generate -semigroup on the space of initial conditions, such that local stable and unstable manifolds can be constructed for a fully nonlinear problems with help of usual methods of the theory of parabolic equations.
Some applications of fractional calculus to operator semigroups and functional calculus
We survey some recent results on functional calculus for generators of holomorphic semigroups, which have been obtained using versions of fractional derivation of Riemann-Liouville or Weyl type. Such a calculus allows us to give tight estimates even in concrete L¹ examples.
Some condensation theorems for semigroup operators.
Some Landau's type inequalities for infinitesimal generators.
Some properties of weighted Sobolev spaces in