This book presents a detailed and contemporary account of the classical theory of
convergence of semigroups and its more recent development treating the case where the …

We present several sufficient conditions for exponential stability and dichotomy of solutions
of the evolution equation uH t A tut à on a Banach space X. Our main theorem says that if the …

The paper is devoted to the problem of existence of propagators for an abstract linear non-
autonomous evolution Cauchy problem of hyperbolic type in separable Banach spaces. The …

We establish general product formulas for the solutions of non-autonomous abstract Cauchy
problems. The main technical tools are evolution semigroups allowing the direct application …

The paper is devoted to study of linear evolution equation corresponding to a small non‐
autonomous Hölder continuous perturbations of Gibbs semigroups on a separable Hilbert …

In this article we prove new results concerning the existence and various properties of an
evolution system UA+ B (t, s) 0⩽ s⩽ t⩽ T generated by the sum−(A (t)+ B (t)) of two linear …

In this article we provide a set of sufficient conditions that allow a natural extension of
Chernoff's product formula to the case of certain one-parameter family of functions taking …

We present adiabatic theorems with and without spectral gap condition for operators A (t): D
(A (t))⊂ X→ X in a Banach space X. In the case with spectral gap, the considered spectral …

We consider linear evolution corresponding to non-autonomous Gibbs semigroup on a
separable Hilbert space ℌ. It is shown that evolution family {U (t, s)} 0≤ s≤ t≤ T solving the …

We prove the well-posedness of non-autonomous linear evolution equations for generators
A (t): D (A (t)) ⊂ X → XA (t): D (A (t))⊂ X→ X whose pairwise commutators are complex …