On an integral operator between Bloch-type spaces on the unit ball

AbstractWe characterize the boundedness and compactness of the following integral-type operatorIφg(f)(z)=∫01Rf(φ(tz))g(tz)dtt,z∈B, where g is a holomorphic function on the unit ball B⊂Cn such that g(0)=0, and φ is a holomorphic self-map of B, acting from α-Bloch spaces to Bloch-type spaces on B

Solvability of some classes of nonlinear first-order difference equations by invariants and generalized invariants

[[abstract]]We introduce notion of a generalized invariant for difference equations, which naturally generalizes notion of an invariant for the equations. Some motivations, basic examples and methods for application of invariants in the theory of solvability of difference equations are given. By using an invariant, as well as, a generalized invariant it is shown solvability of two classes of nonlinear first-order difference equations of interest, for nonnegative initial values and parameters appearing therein, considerably extending and explaining some problems in the literature. It is also explained how these classes of difference equations can be naturally obtained from some linear second-order difference equations with constant coefficients. [ABSTRACT FROM AUTHOR] Copyright of Electronic Journal of Qualitative Theory of Differential Equations is the property of Bolyai Institute and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.

On the recursive sequence x

We investigate the periodic character of solutions of the nonlinear difference equation xn+1=−1/xn+A/xn−1. We give sufficient conditions under which every positive solution of this equation converges to a period two solution. This confirms a conjecture in the work of DeVault et al. (2000)

Solvability of thirty-six three-dimensional systems of difference equations of hyperbolic-cotangent type

We present thirty-six classes of three-dimensional systems of difference equations of the hyperbolic-cotangent type which are solvable in closed form

On some classes of solvable difference equations related to iteration processes

We present several classes of nonlinear difference equations solvable in closed form, which can be obtained from some known iteration processes, and for some of them we give some generalizations by presenting methods for constructing them. We also conduct several analyses and give many comments related to the difference equations and iteration processes

Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane

Here we introduce the nth weighted space on the upper half-plane Π+={z∈ℂ:Im z>0} in the complex plane ℂ. For the case n=2, we call it the Zygmund-type space, and denote it by 𝒵(Π+). The main result of the paper gives some necessary and sufficient conditions for the boundedness of the composition operator Cφf(z)=f(φ(z)) from the Hardy space Hp(Π+) on the upper half-plane, to the Zygmund-type space, where φ is an analytic self-map of the upper half-plane

Composition operators from the weighted . . .

The boundedness of the composition operator from the weighted Bergman space to the recently introduced by the author, the nth weighted space on the unit disc, is characterized. Moreover, the norm of the operator in terms of the inducing function and weights is estimated

On Bloch-type functions with Hadamard gaps

We give some sufficient and necessary conditions for an analytic function f on the unit ball B with Hadamard gaps, that is, for ,∞ as well as to the corresponding little space. A remark on analytic functions with Hadamard gaps on mixed norm space on the unit disk is also given