Matrix transformations of sequences and applications in Fourier analysis

Abstract

In the presented paper we consider a sequence and its Nörlud and a generalized mean derived from a matrix transformation. Furthermore, sufficient conditions for the matrix are found which implies the converges of the generalized matrix means from the Nörlud ones. The results drawn make it possible to transfer well-known theorems in the theory of Fourier series to more general sequences of operators.

Keywords

• Walsh-Paley system
• Walsh-Kaczmarz system
• Trigonometric system
• Vilenkin system
• Almost everywhere convergence
• Numerical sequences