Let D be the open unit disk in the complex plane C. Denote by H(D) the class of all functions analytic on D. An analytic self-map φ : D → D induces the composition operator Cφ on H(D), defined by Cφ ( f ) = f (φ(z)) for f analytic on D. It is a well-known consequence of Littlewood’s subordination principle that the composition operator Cφ is bounded on the classical Hardy and Bergman spaces (se...

Given two analytic nonlinear input-output systems represented as Fliess operators, four system interconnections are considered in a unified setting: the parallel connection, product connection, cascade connection and feedback connection. In each case, the corresponding generating series is produced, when one exists, and conditions for convergence of the corresponding Fliess operator are given. ...

The theory of c-frames and c-Bessel mappings are the generalizationsof the theory of frames and Bessel sequences. In this paper, weobtain several equivalent conditions for dual of c-Bessel mappings.We show that for a c-Bessel mapping $f$, a retrievalformula with respect to a c-Bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-Besselmapping which  wea...

We consider a generalized connection in three dimensions and show that it emerges in Chern-Simons-Maxwell theories when one studies the disorder instanton operator. We generalized this construction to non-Abelian theories and find that the disorder operator (the ’t Hooft operator) is equivalent to a generalized Wilson loop in a representation that depends on the Chern-Simons term. We speculate ...

where dA is the normalized area measure in D. The case where α = 0 is known as the (unweighted) Bergman space, often simply denoted by A2. Let φ be an analytic map from the open unit disk D into itself. The operator that takes the analytic map f to f ◦ φ is a composition operator and is denoted by Cφ . A natural generalization of a composition operator is an operator that takes f to ψ · f ◦ φ, ...

The purpose of this paper is to introduce and study a new kind of generalized strongly nonlinear operator inclusion problems involving generalized m-accretive mapping in Banach spaces. By using the resolvent operator technique for generalized m-accretive mapping due to Huang and Fang, we also prove the existence theorem of the solution for this kind of operator inclusion problems and construct ...

We study a generalized Chebyshev oscillator associated with point interaction for the discrete Schrödinger equation. Our goal is to find realization of annihilation operator this by differential operator. This can be used obtain equation corresponding polynomials.

We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS. Thereafter, non-asymptotic high-probability bounds are established on the e...

Program composition and compositional proof systems have proven them­ selves important for simplifying the design and the verification of programs. The paper presents a version of the jigsaw program composition operator pre­ viously defined in [FFG90, FFG91]. Here, the jigsaw operator is defined as the unification of its components by their most general unifier. The jigsaw operator generalizes ...