On the Schrödinger equation in L...spaces.
On the Schrödinger heat kernel in horn-shaped domains
We prove pointwise lower bounds for the heat kernel of Schrödinger semigroups on Euclidean domains under Dirichlet boundary conditions. The bounds take into account non-Gaussian corrections for the kernel due to the geometry of the domain. The results are applied to prove a general lower bound for the Schrödinger heat kernel in horn-shaped domains without assuming intrinsic ultracontractivity for the free heat semigroup.
On the spectral bound of the generator of a -semigroup
We give several conditions implying that the spectral bound of the generator of a -semigroup is negative. Applications to stability theory are considered.
On the spectral properties of translation operators in one-dimensional tubes
We study the spectral properties of some group of unitary operators in the Hilbert space of square Lebesgue integrable holomorphic functions on a one-dimensional tube (see formula (1)). Applying the Genchev transform ([2], [5]) we prove that this group has continuous simple spectrum (Theorem 4) and that the projection-valued measure for this group has a very explicit form (Theorem 5).
On the stability of differentiability of semigroups.
On the Surjective Dunford-Pettis Property.
On the surjective Dunford-Pettis property
On the topology induced by the adjoint of a semigroup of operators.
On the well-posedness of the heat equation on unbounded domains.
One-parameter semigroups in the convolution algebra of rapidly decreasing distributions
The paper is devoted to infinitely differentiable one-parameter convolution semigroups in the convolution algebra of matrix valued rapidly decreasing distributions on ℝⁿ. It is proved that is the generating distribution of an i.d.c.s. if and only if the operator on satisfies the Petrovskiĭ condition for forward evolution. Some consequences are discussed.
Operator theoretic properties of semigroups in terms of their generators
Let be a C₀ semigroup with generator A on a Banach space X and let be an operator ideal, e.g. the class of compact, Hilbert-Schmidt or trace class operators. We show that the resolvent R(λ,A) of A belongs to if and only if the integrated semigroup belongs to . For analytic semigroups, implies , and in this case we give precise estimates for the growth of the -norm of (e.g. the trace of ) in terms of the resolvent growth and the imbedding D(A) ↪ X.
Optimal properties of contraction semigroups in Banach spaces.
Optimal regularization method for ill-posed Cauchy problems.
Optimal time and space regularity for solutions of degenerate differential equations
We derive optimal regularity, in both time and space, for solutions of the Cauchy problem related to a degenerate differential equation in a Banach space X. Our results exhibit a sort of prevalence for space regularity, in the sense that the higher is the order of regularity with respect to space, the lower is the corresponding order of regularity with respect to time.
Optimization problems for structural acoustic models with thermoelasticity and smart materials
Optimization problem for a structural acoustic model with controls governed by unbounded operators on the state space is considered. This type of controls arises naturally in the context of "smart material technology". The main result of the paper provides an optimal synthesis and solvability of associated nonstandard Riccati equations. It is shown that in spite of the unboundedness of control operators, the resulting gain operators (feedbacks) are bounded on the state space. This allows to provide...
Pairs of function spaces and exponential dichotomy on the real line.
Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses
In this paper, we consider periodic solutions for a class of nonlinear evolution equations with non-instantaneous impulses on Banach spaces. By constructing a Poincaré operator, which is a composition of the maps and using the techniques of a priori estimate, we avoid assuming that periodic solution is bounded like in [1-4] and try to present new sufficient conditions on the existence of periodic mild solutions for such problems by utilizing semigroup theory and Leray-Schauder's fixed point theorem....
Periodic solutions for some partial functional differential equations.
Periodic systems dependent on parameters.
Periodicity and almost periodicity in Markov lattice semigroups