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Über eine Verallgemeinerung eines Resultats von Riesz über trigonometrische Polynome auf allgemeine bandbegrenzte Funktionen
Author(s) -
Boche H.,
Wunder G.
Publication year - 2002
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200205)82:5<347::aid-zamm347>3.0.co;2-1
Subject(s) - mathematics , bounded function , bounding overwatch , interpolation (computer graphics) , upper and lower bounds , function (biology) , mathematical analysis , pure mathematics , combinatorics , physics , computer science , motion (physics) , classical mechanics , artificial intelligence , evolutionary biology , biology
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.