Search

This paper aims to obtain decompositions of higher dimensional functions into sums of non-tangential boundary limits of the corresponding Hardy space functions on tubes for the index range . In the one-dimensional case, Deng and Qian recently obtained such a Hardy space decomposition result: for any function , there exist functions and such that , where and are, respectively, the non-tangential boundary limits of some Hardy space functions in the upper-half and lower-half planes. In the present paper, we generalize the one-dimensional Hardy space decomposition result to the higher dimensions and discuss the uniqueness issue of such decomposition. [ABSTRACT FROM AUTHOR]

In this paper we consider Hardy space decomposition ofwherestands for the open unit disc, andis its boundary. Hardy spaces decompositions forandforare, as classical results, available in the literature. Forthe basic tools are the Plemelj formula and the boundedness of the Hilbert transformation. Forneither on the real line, nor on the unit circle, a Plemelj formula, or Hilbert transformation are available. In a recent paper Deng and Qian obtain Hardy spaces decomposition foron the real line by means of rational approximation. In the present paper by using rational functions, we achieve the same goal forfor the rangeThe work on the unit circle exposes the particular features of the kind of decomposition in the compact situation adaptable to higher dimensions. [ABSTRACT FROM AUTHOR]

This paper applies Nevanlinna theory of value distribution to discuss existence of solutions of certain types of nonlinear differential-difference equations such as (5) and (8) given in the succeeding paragraphs. Existence of solutions of differential equations and difference equations can be said to have been well studied, that of differential-difference equations, on the other hand, have been paid little attention. Such mixed type equations have great significance in applications. This paper, in particular, generalizes the Rellich-Wittich-type theorem and Malmquist-type theorem about differential equations to the case of differential-difference equations. [ABSTRACT FROM AUTHOR]