Über eine verallgemeinerung eines resultats von riesz über trigonometrische polynome auf allgemeine bandbegrenzte funktionen

In this paper the behaviour of bounded, bandlimited functions in the neighborhood of an extremum is characterized. In particular, an upper bound on the peak magnitude is derived provided that the function is bounded on oversampling sets. Moreover, it is shown that in this situation an extremal function exists. The question of bounding of band-limited functions naturally arises in interpolation theory and is also of fundamental importance in communication engineering.