In this paper we consider a nonuniform unstability concept for evolution operators in Banach spaces. The relationship between this concept and the Perron condition is studied. Generalizations to the nonuniform case of some results of Van Minh, Räbiger and Schnaubelt are obtained. The theory we present here is applicable for general time varying linear equations in Banach spaces. 1. Evolution op...

Factorable M{dimensional lters are interesting because they can be implemented e ciently: their computational complexity is O(Mn) instead of O(n ) (as in the case of generic non{factorable lters). Unfortunately, the pass{band support of a factorable lter can assume only very simple shapes (parallelepipeds with edges pairwise parallel to the axes), which are not adequate for most applications. I...

Abstract Let u be an analytic function in the unit disk $\mathbb{D}$ D and φ self-map of . We give characterizations symbols for which multiplication operator $M_{u}$ M u weighted composition $M_{u,\varphi }$ , φ</mml...

We consider rank one perturbations Aα = A+α( · , φ)φ of a self-adjoint operator A with cyclic vector φ ∈ H−1(A) on a Hilbert space H. The spectral representation of the perturbed operator Aα is given by a singular integral operator of special form. Such operators exhibit what we call ’rigidity’ and are connected with two weight estimates for the Hilbert transform. Also, some results about two w...

Let X be an operator space, let φ be a product on X , and let (X, φ) denote the algebra that one obtains. We give necessary and sufficient conditions on the bilinear mapping φ for the algebra (X, φ) to have a completely isometric representation as an algebra of operators on some Hilbert space. In particular, we give an elegant geometrical characterization of such products by using the Haagerup ...

Motivated by searching for positive radially symmetric solutions in a fixed exterior domain in RN for partial differential equations involving the curvature operator, the global positiveness and uniqueness of (*) is also considered. Several examples illustrate the discrepancies between the bounded and unbounded Φ. The results for the curvature operator and the classical Φ-Laplacian are compared...

We propose to strengthen standard factorable relaxations of global optimization problems through the use of functional transformations of intermediate expressions. In particular, we exploit convex transformability of the component functions of factorable programs as a tool in the generation of bounds. We define suitable forms of transforming functions and assess, theoretically and computational...

Let ζ and η be distinct points on the unit circle and suppose that φ is a linear-fractional self-map of the unit disk D, not an automorphism, with φ(ζ) = η. We describe the C-algebra generated by the associated composition operator Cφ and the shift operator, acting on the Hardy space on D.

Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz continuous φ-strongly accretive operator or uniformly continuous φ-strongly accretive operator. We prove that under different conditions the three-step iteration methods with errors converge strongly to the solution of the equation Tx = f for a given f ∈ X.

The paper considers representing bilinear forms by linear operators in the case of a Krull valuation. More precisely, after making some suitable assumptions, we prove that if φ is a non-degenerate bilinear form, then φ is representable by a unique linear operator A whose adjoint operator A∗ exists.