Harmonic functions on the disk and regular matrix summability

Harmonic Functions in the Unit Disk

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On absolute matrix summability methods

On Absolute Matrix Summability Methods

We have proved a theorem on |T, p n | k summability methods. This theorem includes a known theorem.

Harmonic and Superharmonic Majorants on the Disk

We prove that a positive function on the unit disk admits a harmonic majorant if and only if a certain explicit upper envelope of it admits a superharmonic majorant. We provide examples to show that mere superharmonicity of the data does not help with the problem of existence of a harmonic majorant. 1. Definitions and statements Let D stand for the open unit disk in the complex plane, and H(D) ...

On the Summability of Bivariate Rational Functions

We present criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q-)differences of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated, first, in terms of single sums and, finally, in terms of values of special functions.