Multiplier algebras, Banach bundles, and one-parameter semigroups
Multipliers of the Hardy space H¹ and power bounded operators
We study the space of functions φ: ℕ → ℂ such that there is a Hilbert space H, a power bounded operator T in B(H) and vectors ξ, η in H such that φ(n) = ⟨Tⁿξ,η⟩. This implies that the matrix is a Schur multiplier of B(ℓ₂) or equivalently is in the space (ℓ₁ ⊗̌ ℓ₁)*. We show that the converse does not hold, which answers a question raised by Peller [Pe]. Our approach makes use of a new class of Fourier multipliers of H¹ which we call “shift-bounded”. We show that there is a φ which is a “completely...
Neutral functional differential equations of second-order with infinite delays.
New approach to streaming semigroups with dissipative boundary conditions.
New approach to streaming semigroups with multiplying boundary conditions.
New characterizations of asymptotic stability for evolution families on Banach spaces.
New classes of analytic and Gevrey semigroups and applications
We consider the operator on a complex Hilbert space, where is positive self-adjoint and is self-adjoint, and where, moreover, « is comparable to , », in a technical sense. Two applications are given.
New spectral criteria for almost periodic solutions of evolution equations
We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...
Non autonomous evolution operators of hyperbolic type.
Non-autonomous inhomogeneous boundary Cauchy problems.
Non-autonomous retarded differential equations: the variation of constants formulas and the asymptotic behaviour.
Non-autonomous stochastic Cauchy problems in Banach spaces
We study the non-autonomous stochastic Cauchy problem on a real Banach space E, , t ∈ [0,T], U(0) = u₀. Here, is a cylindrical Brownian motion on a real separable Hilbert space H, are closed and densely defined operators from a constant domain (B) ⊂ H into E, denotes the generator of an evolution family on E, and u₀ ∈ E. In the first part, we study existence of weak and mild solutions by methods of van Neerven and Weis. Then we use a well-known factorisation method in the setting of evolution...
Non-commutative symmetric Markov semigroups.
Nonlinear elliptic systems with dynamic boundary conditions.
Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition
The aim of the present paper is to investigate the global existence of mild solutions of nonlinear mixed Volterra-Fredholm integrodifferential equations, with nonlocal condition. Our analysis is based on an application of the Leray-Schauder alternative and rely on a priori bounds of solutions.
Nonlinear perturbations of postive semigroups.
Nonlocal quasilinear damped differential inclusions.
(Nonsymmetric) Dirichlet operators on : existence, uniqueness and associated Markov processes
Non-Symmetric Translation Invariant Dirichlet Forms.
Non-unitary scattering and capture. II. Quantum dynamical semigroup theory