We give examples of composition operators CΦ on H(D) showing that the condition ‖Φ‖∞ = 1 is not sufficient for their approximation numbers an(CΦ) to satisfy limn→∞[an(CΦ)] √ n = 1, contrary to the 1-dimensional case. We also give a situation where this implication holds. We make a link with the Monge-Ampère capacity of the image of Φ. Key-words : approximation numbers; Bergman space; bidisk; co...

We study the intertwining relation XTφ = TψX where Tφ and Tψ are the Toeplitz operators induced on the Hardy space H 2 by analytic functions φ and ψ, bounded on the open unit disc U, and X is a nonzero bounded linear operator on H. Our work centers on the connection between intertwining and the image containment ψ(U) ⊂ φ(U), as well as on the nature of the intertwining operator X. We use our re...

Let φ be a holomorphic self-map of a bounded homogeneous domain D in C. In this work, we show that the composition operator Cφ : f 7→ f ◦ φ is bounded on the Bloch space B of the domain and provide estimates on its operator norm. We also give a sufficient condition for φ to induce an isometry on B. This condition allows us to construct non-trivial examples of isometric composition operators in ...

Let D be the open unit disk in the complex plane C, H(D) the class of all analytic functions on D and φ an analytic self-map of D. In order to unify the products of composition, multiplication, and differentiation operators, Stević and Sharma introduced the following so-called Stević-Sharma operator on H(D): Tψ1,ψ2,φf(z) = ψ1(z)f(φ(z)) + ψ2(z)f ′(φ(z)), where ψ1, ψ2 ∈ H(D). By constructing some...

A prevalent strategy in vector field data analysis is to extract and classify the integral curves derived from flow data. With the exception of topology-based methods, many of these classifications depend on the choice of algorithm thresholds. However, topology-based methods have yet to be fully developed for time-varying vector field analysis. In this paper, we introduce a novel descriptor, ca...

We provide in this work sufficient conditions for existence and multiplicity of positive unbounded solutions a class singular second-order boundary value problem associated with φ-Laplacian operator posed on the half-line. The proofs are based theorem cone expansion compression Banach space.

Primarily guided with the idea to express zero-time transitions by means of temporal propositional language, we have developed a temporal logic where the time flow is isomorphic to ordinal ω 2 (concatenation of ω copies of ω). If we think of ω 2 as lexicographically ordered ω×ω, then any particular zero-time transition can be represented by states whose indices are all elements of some {n} × ω....

On a compact manifold with boundary, consider the realization B of an elliptic, possibly pseudodifferential, boundary value problem having a spectral cut (a ray free of eigenvalues), say R − . In the first part of the paper we define and discuss in detail the operator logB; its residue (generalizing the Wodzicki residue) is essentially proportional to the zeta function value at zero, ζ(B, 0), a...

A characterisation of the generators of quantum stochastic cocy-cles of completely positive (CP) maps is given in terms of the complete dissipa-tivity (CD) of its form-generator. The pseudo-Hilbert dilation of the stochastic form-generator and the pre-Hilbert dilation of the corresponding dissipator is found. The general form of the linear continuous structural maps for the algebra of all bound...