Let φ be an analytic map of unit disk D into itself, consider the composition operator Cφ defined by Cφ(f) = f◦φ whenever f is analytic on D. In this paper, we discuss necessary and sufficient conditions under which a composition operator on a large class of weighted Hardy spaces is a compact.

This talk is mainly concerned with two generalizations of convergence of sequences called I-convergence and I∗-convergence. We will mention some other generalizations of limit which are related to I-convergence, e.g Banach limit and statistical convergence. 1 Generalizations of limit The notion of limit is one of the central notions in mathematical analysis. No wonder it was generalized by math...

A minimally 1-factorable cubic bigraph is a graph in which every 1-factor lies in precisely one 1-factorization. The author investigates determinants and permanents of such graphs and, in particular, proves that the determinant of any minimally 1-factorable cubic bigraph of girth 4 is 0.

Quantum operations frequently occur in quantum measurement theory, quantum probability, quantum computation and quantum information theory. If an operator A is invariant under a quantum operation φ we call A a φ-fixed point. Physically, the φ-fixed points are the operators that are not disturbed by the action of φ. Our main purpose is to answer the following question. If A is a φ-fixed point, i...

The purpose of this article is to establish the existence of multiple positive solutions of the dynamic equation on time scales φ uΔ t ∇ h t f t, u t , uΔ t 0, t ∈ 0, T T , subject to the multipoint boundary condition uΔ 0 0, u T ∑m−2 i 1 aiu ξi , where φ : R → R is an increasing homeomorphism and satisfies the relation φ xy φ x φ y for x, y ∈ R, which generalizes the usually p-Laplacian operat...

Characterizations of the stability and orthonormality of a multivariate matrix refinable function Φ with arbitrary matrix dilation M are provided in terms of the eigenvalue and 1-eigenvector properties of the restricted transition operator. Under mild conditions, it is shown that the approximation order of Φ is equivalent to the order of the vanishing moment conditions of the matrix refinement ...

one can quantize an invertible symbol σ ∈ C∞(S∗X; hom(π∗E, π∗F )) as an elliptic pseudodifferential operator in the Φ-b or edge calculus, ΨΦ-b(X;E,F ), introduced in [7] or alternately as an elliptic operator in the Φ-c or φ calculus, ΨΦ-c(X;E,F ), introduced in [8]. As on a closed manifold, either of these operators will induce a bounded operator acting between natural L-spaces of sections but...

and Applied Analysis 3 Next we present auxiliary statements which play important roles in proving the main results. Define F : 0,∞ → R by F x Φ x/q−1/q −Φ 1−1/x and h : Φ −∞ q ,∞ → R by h x x 1 − q1−α [ 1 − ( 1 ( q − 1 ) Φ−1 x )1−α] . 2.1 For y : q0 → R \ {0} define the operator L by L [ y ] t Φ ( y ( q2t ) qy ( qt ) − 1 q ) −Φ ( 1 − y t

In the operator algebraic formulation of probability theory Markov processes typically appear as perturbations of Bernoulli processes. We develop a scattering theory for this situation. This theory applies to the isomorphism problem between Markov processes and Bernoulli shifts as well as to the description of open quantum systems. Introduction. The need to extend classical probability theory i...