Non-unitary scattering and capture. II. Quantum dynamical semigroup theory
Norm continuity of -semigroups
We show that a positive semigroup on with generator A and ||R(α + i β)|| → 0 as |β| → ∞ for some α ∈ ℝ is continuous in the operator norm for t>0. The proof is based on a criterion for norm continuity in terms of “smoothing properties” of certain convolution operators on general Banach spaces and an extrapolation result for the -scale, which may be of independent interest.
Norms for copulas.
Note on analytic regularity of heat kernels on nilpotent Lie groups
Let G be the simplest nilpotent Lie group of step 3. We prove that the densities of the semigroup generated by the sublaplacian on G are not real-analytic.
Note on multiplicative perturbation of local -regularized cosine functions with nondensely defined generators.
Notes on Analytic Convoluted -semigroups
Notes on the propagators of evolution equations.
Numerical exponential decay to dissipative Bresse system.
On a class of abstract degenerate fractional differential equations of parabolic type
In this paper, we investigate a class of abstract degenerate fractional differential equations with Caputo derivatives. We consider subordinated fractional resolvent families generated by multivalued linear operators, which do have removable singularities at the origin. Semi-linear degenerate fractional Cauchy problems are also considered in this context.
On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions
We study a new class of Markov type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space E. Our results allow us to characterize the generators of Markov transition semigroups in infinite dimensions such as the heat and the Ornstein-Uhlenbeck semigroups.
On a Class of Retarded Partial Differential Equations.
On a Class of Time Inhomogeneous Nonsingular Flows and Schrödinger Operators.
On a functional equation with derivative and symmetrization
We study existence, uniqueness and form of solutions to the equation where α, β, γ and f are given, and stands for the even part of a searched-for differentiable function g. This equation emerged naturally as a result of the analysis of the distribution of a certain random process modelling a population genetics phenomenon.
On a higher-order evolution equation with a Stepanov-bounded solution.
On a local ergodic theorem
On a mild solution of a semilinear functional-differential evolution nonlocal problem.
On a model for quantum friction. I. Fermi's golden rule and dynamics at zero temperature
On a non-linear semi-group associated with stochastic optimal control and its excessive majorant
On a regularizing effect of Schrödinger type groups
On a theorem of H. P. Lotz on quasi-compactness of Markov operators