�ber die Fourierkoeffizienten einer stetigen Funktion von beschr�nkter Schwankung

Abstract

Fiir die Fourierkoeffizienten a,, b, einer im Intervall (0,2~) deftnierten Funk~ion yon beschr~nkter Schwankung f(x) gilt bekanntlich: mit andern Worten: die Produkt~erte ~a, und rib, sind in ihrer Gesamtheir beschr~nkt. Andererseits abet ist nicht notwendig zugleich

Analysis and Probability Wavelets, Signals, Fractals

“…Some relevant references (books and papers) covering Riesz products are [Riel8,Mey79], and a list covering related infinite-product constructs includes the following:…”

The Grothendieck Factorization Theorem

“…But if A is infinite, then the object represented by (5.50) will depend on x P C A , as well as the mode of convergence of the series in (5.50). The construct in (5.49), which appeared first in the circle group setting -with lacunary exponentials in place of Rademacher characters (Riesz, 1918) -is known as a Riesz product.…”

“…We make use of two classical scenarios that originated in Salem and Zygmund (1947) and Riesz (1918).…”

Multiscale Riesz Products and their Support Properties

“…In his 1918 paper, "Über die Fourierkoeffizienten einer stetigen Funktion von beschränkter Schwankung" [33], Riesz proved the existence of a continuous function F of bounded variation on T, whose Fourier-Stieltjes coefficients do not vanish at infinity. His example essentially was the pointwise limit of the functions…”