On the ergodic limits for unitary periodic propagators.
On the existence and uniqueness of solutions for an incomplete second-order abstract Cauchy problem
We prove existence and uniqueness of classical solutions for an incomplete second-order abstract Cauchy problem associated with operators which have polynomially bounded resolvent. Some examples of differential operators to which our abstract result applies are also included.
On the exponential stability and dichotomy of -semigroups
A characterization of exponentially dichotomic and exponentially stable -semigroups in terms of solutions of an operator equation of Lyapunov type is presented. As a corollary a new and shorter proof of van Neerven’s recent characterization of exponential stability in terms of boundedness of convolutions of a semigroup with almost periodic functions is given.
On the Gelfand-Hille theorems
On the generation of non-continuous semigroups.
On the growth of analytic semigroups along vertical lines
We construct two Banach algebras, one which contains analytic semigroups such that arbitrarily slowly as , the other which contains ones such that arbitrarily fast
On the hypercontractivity property.
On the invertibility of isometric semigroup representations
Let T be a representation of a suitable abelian semigroup S by isometries on a Banach space. We study the spectral conditions which will imply that T(s) is invertible for each s in S. On the way we analyse the relationship between the spectrum of T, Sp(T,S), and its unitary spectrum . For or , we establish connections with polynomial convexity.
On the iterated Green functions on a bounded domain and their related Kato class of potentials.
On the Kantorovich-Rubinstein maximum principle for the Fortet-Mourier norm
A new version of the maximum principle is presented. The classical Kantorovich-Rubinstein principle gives necessary conditions for the maxima of a linear functional acting on the space of Lipschitzian functions. The maximum value of this functional defines the Hutchinson metric on the space of probability measures. We show an analogous result for the Fortet-Mourier metric. This principle is then applied in the stability theory of Markov-Feller semigroups.
On the lattice boundary of Markov operators
On the local ergodic theorems of Krengel, Kubokawa, and Terrell
On the mild solutions of higher-order differential equations in Banach spaces.
On the modulus of one-parameter semigroups.
On the nonlocal Cauchy problem for semilinear fractional order evolution equations
In this paper, we develop the approach and techniques of [Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam. Systems Appl., 2007, 16(3), 507–516], [Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations, Nonlinar Anal. Real World Appl., 2010, 11(5), 4465–4475] to deal with nonlocal Cauchy problem for semilinear fractional order evolution equations. We present two new sufficient conditions on existence of mild solutions. The first...
On the operator equation with unbounded operators , , and .
On the Perron problem for the exponential dichotomy of -semigroups.
On the Perron-Frobenius theory for sets of positive operators
On the Perturbation Theory for Strongly Continuous Semigroups.
On the positivity of semigroups of operators
In a Banach space , let be a -semigroup with generating operator . For a cone ...