The power (−A)b, b ∈ C is defined for a closed linear operator A whose resolvent is polynomially bounded on the region which is, in general, strictly contained in an acute angle. It is proved that all structural properties of complex powers of densely defined operators with polynomially bounded resolvent remain true in the newly arisen situation. The fractional powers are considered as generato...

Within convex analysis, a rich theory with various applications has been evolving since the proximal average of convex functions was first introduced over a decade ago. When one considers the subdifferential of the proximal average, a natural averaging operation of the subdifferentials of the averaged functions emerges. In the present paper we extend the reach of this averaging operation to the...

In this note self-adjoint realizations of second order elliptic differential expressions with non-local Robin boundary conditions on a domain Ω ⊂ Rn with smooth compact boundary are studied. A Schatten–von Neumann type estimate for the singular values of the difference of the mth powers of the resolvents of two Robin realizations is obtained, and for m > n 2 − 1 it is shown that the resolvent p...

The paper studies the non-selfadjoint linear differential operator Ly = d dt ( (1−acos t)y+bsin t dy dt ) acting in the Hilbert space L2(−π,π) that originated from a steady state stability problem in fluid dynamics. The operator L is of Heun type and involves two parameters a,b related to the hydrostatic pressure and capillary properties of the fluid. The results concern (1) the properties of f...

In this paper we discuss the characteristic property of the left invertible semigroups on general Banach spaces and admissibility of the observation operators for such semigroups. We obtain a sufficient and necessary condition about their generators. Further, for the left invertible and exponentially stable semigroup in Hilbert space we show that there is an equivalent norm under which it is co...

We consider the operator T = m k=1 A 1k ⊗ A 2k (1 ≤ m < ∞), where A lk are n l × n l matrices (k = 1,. .. , m; l = 1, 2), ⊗ means the tensor product. Norm estimates for the resolvent of that operator are derived. By these estimates, we obtain bounds for a solution X of the equation m k=1 A 1k X A 2k = C and explore perturbations of that equation. The norm estimates for the resolvent of T enable...

We consider the question: To what extend does the Weyl function (i.e., the abstract Dirichlet-to-Neumann map) see the same singularities as the resolvent of some restriction of the maximal operator. The proper, so-called detectable, subspace will be introduced and analyzed for particular examples, such as, Schrodinger operators, Hain–Lust operators, and (if time permits), the Friedrichs model o...

Let A be a sectorial operator on a non-atomic Lp-space, 1 ≤ p < ∞, whose resolvent consists of integral operators, or more generally, has a diffuse representation. Then the fractional domain spaces D(Aα) for α ∈ (0, 1) do not coincide with the real interpolation spaces of (Lq , D(A)). As a consequence, we obtain that no such operator A has a bounded H∞-calculus if p = 1.

Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multipliers theorems, we obtain necessary and sufficient conditions to guarantee existence and uniqueness of periodic solutions to the equation d dt (Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our res...