Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Real and Complex Analysis

The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

Generalized composition operators on zygmund spaces and bloch type spaces

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Aufgaben und Lehrsätze aus der Analysis

In this paper we investigate the relationship among the following integrals ∫ B | u ( x ) | p - i | ∇ u ( x ) | i ( 1 - | x | ) α d V ( x ) , where i ∈ { 0 , 1 , 2 } , 1 0 , and where u is an arbitrary harmonic function on the unit ball B ⊂ R n . Growth of the integral means of harmonic functions is also compared to the integral means of their gradient.

/pdf/area-type-inequalities-and-integral-means-of-harmonic-36e67aex4a.pdf

Area type inequalities and integral means of harmonic functions on the unit ball

Solvability and semi-cycle analysis of a class of nonlinear systems of difference equations

Abstract The boundedness of the weighted differentiation composition opera- tor from the logarithmic Bloch space to the weighted-type space is characterized in terms of the sequence (zn)n∈N0. An asymptotic estimate of the essential norm of the operator is also given in terms of the sequence, which gives a characterization for the compactness of the operator.

/pdf/weighted-differentiation-composition-operators-from-the-15rkxr7dtr.pdf

Weighted differentiation composition operators from the logarithmic Bloch space to the weighted-type space

We study the boundedness and compactness of the weighted composition
operators as well as integral-type operators between weighted Hardy spaces on the unit ball.

/pdf/weighted-composition-operators-and-integral-type-operators-4yts5kdzjc.pdf

Stevo Stević

Papers

Area type inequalities and integral means of harmonic functions on the unit ball

Solvability and semi-cycle analysis of a class of nonlinear systems of difference equations

Weighted differentiation composition operators from the logarithmic Bloch space to the weighted-type space

Weighted Composition Operators and Integral-Type Operators between Weighted Hardy Spaces on the Unit Ball

Extended Cèsaro operators between mixed-norm spaces and Bloch-type spaces in the until ball