51. The Expression of Trigonometrical Series in Fourier Form
- Author
-
George Cross
- Subjects
Pure mathematics ,symbols.namesake ,Fourier transform ,Series (mathematics) ,General Mathematics ,Bounded function ,010102 general mathematics ,symbols ,Countable set ,0101 mathematics ,Expression (computer science) ,01 natural sciences ,Mathematics - Abstract
In a paper published in 1936 Burkill (2) proved that, if the trigonometrical series1.1is bounded except on a countable set and if the series obtained by integrating series (1.1) once converges everywhere, then the coefficients can be written in Fourier form using the C1P-integral. In §3 of this paper an analogous result is shown to be true when (1.1) is bounded (C, k), k < 0. The proof of this depends on generalizations of theorems by Verblunsky and Zygmund and both of these generalizations are obtained in §2.
- Published
- 1960