Integral Superposition-Type Operators on Some Analytic Function Spaces

All entire functions which transform a class of holomorphic Zygmund-type spaces into weighted analytic Bloch space using the so-called n -generalized superposition operator are characterized in this paper. Moreover, certain specific properties such as boundedness and compactness of the newly defined class of generalized integral superposition operators are discussed and established by using the concerned entire functions.

On the Lattice of ESI-closed Classes of Multifunctions on Two-elements Set

The paper considers multifunctions on a two-element set with superposition and the equality predicate branching operator. The superposition operator is based on the intersection of sets. The main purpose of the work is to describe all closed classes with respect to the considered operators. The equality predicate branching operator allows the task to be reduced to a description of all closed classes generated by 2-variable multifunctions. Using this, it is shown that the lattice of classes closed with respect to the considered operators contains 237 elements. A generating set is specified for each closed class. The result obtained in the paper extends the known result for all closed classes of partial functions on a two-element set.

Measures of noncompactness and superposition operator in the space of regulated functions on an unbounded interval

In this paper, we formulate necessary and sufficient conditions for relative compactness in the space $$BG({\mathbb {R}}_+,E)$$ B G ( R + , E ) of regulated and bounded functions defined on $${\mathbb R}_+$$ R + with values in the Banach space E. Moreover, we construct four new measures of noncompactness in the space $$BG({\mathbb {R}}_+,E)$$ B G ( R + , E ) . We investigate their properties and we describe relations between these measures. We provide necessary and sufficient conditions so that the superposition operator (Niemytskii) maps $$BG({\mathbb {R}}_+,E)$$ B G ( R + , E ) into $$BG({\mathbb {R}}_+,E)$$ B G ( R + , E ) and, additionally, be compact.

Some inequalities and superposition operator in the space of regulated functions

Some inequalities connected to measures of noncompactness in the space of regulated function R(J, E) were proved in the paper. The inequalities are analogous of well known estimations for Hausdorff measure and the space of continuous functions. Moreover two sufficient and necessary conditions that superposition operator (Nemytskii operator) can act from R(J, E) into R(J, E) are presented. Additionally, sufficient and necessary conditions that superposition operator Ff : R(J, E) → R(J, E) was compact are given.

The superposition operator in the space of functions continuous and converging at infinity on the real half-axis

We will consider the so-called superposition operator in the space CC(ℝ+) of real functions defined, continuous on the real half-axis ℝ+ and converging to finite limits at infinity. We will assume that the function f = f(t, x) generating the mentioned superposition operator is locally uniformly continuous with respect to the variable x uniformly for t ∈ ℝ+. Moreover, we require that the function t → f(t, x) satisfies the Cauchy condition at infinity uniformly with respect to the variable x. Under the above indicated assumptions a few properties of the superposition operator in question are derived. Examples illustrating our considerations will be included.

Orthogonal state of coherent state based on Hermite-excited superposition operator: Production and Wigner function

An orthogonal state of coherent state is produced by applying an orthogonalizer related with Hermite-excited superposition operator [Formula: see text]. Using some technique, we cleverly deal with the normalization and discuss the nonclassical and non-Gaussian characters of the orthogonal state. The analytical expressions for the Wigner functions of the orthogonal state are derived in detail. Numerical results show that the orthogonal state will exhibit its richly nonclassical and non-Gaussian character by changing the interaction parameters.

On characterization of non-Newtonian superposition operators in some sequence spaces

In this paper, we define a non-Newtonian superposition operator NPf where f : N x R(N)? ? R(N)? by NPf (x) = (f(k,xk))? k=1 for every non-Newtonian real sequence x = (xk). Chew and Lee [4] have characterized Pf : ?p ? ?1 and Pf : c0 ? ?1 for 1 ? p < ?. The purpose of this paper is to generalize these works respect to the non-Newtonian calculus. We characterize NPf : ?? (N) ??1(N), NPf: c0(N)??1(N), NPf : c (N)? ?1 (N) and NPf : ?p (N) ? ?1 (N), respectively. Then we show that such NPf : ??(N) ? ?1 (N) is *-continuous if and only if f (k,.) is *-continuous for every k ? N.

Analytic Morrey Spaces and Bloch-Type Spaces

This paper is devoted to characterizing the boundedness of the Riemann-Stieltjes operators from analytic Morrey spaces to Bloch-type spaces. Moreover, the boundedness of the superposition operator and weighted composition operator on analytic Morrey spaces is discussed, respectively.