Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 10, Number 2 (2016), 415-429.
On the existence of universal series by the generalized Walsh system
In this paper, we prove the following: let be a continuous function with and increasing in . Then there exists a series of the form
with the following property: for each a weight function , , can be constructed so that the series is universal in the weighted space both with respect to rearrangements and subseries.
Banach J. Math. Anal., Volume 10, Number 2 (2016), 415-429.
Received: 12 March 2015
Accepted: 22 July 2015
First available in Project Euclid: 19 April 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 42A65: Completeness of sets of functions
Secondary: 42A20: Convergence and absolute convergence of Fourier and trigonometric series 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Episkoposian, Sergo A. On the existence of universal series by the generalized Walsh system. Banach J. Math. Anal. 10 (2016), no. 2, 415--429. doi:10.1215/17358787-3589331. https://projecteuclid.org/euclid.bjma/1461091167