On the structure of universal functions for classes $L^{p}[0,1)^{2},p\in (0,1)$ , with respect to the double Walsh system
| Autor: | M. G. Grigoryan, Artsrun Sargsyan |
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| Rok vydání: | 2019 |
| Předmět: |
Discrete mathematics
Class (set theory) Algebra and Number Theory convergence in metric Existential quantification Universal function Structure (category theory) Fourier coefficients Measure (mathematics) Walsh system universal function Walsh function 42C10 Locally integrable function Fourier series 43A15 Analysis Mathematics |
| Zdroj: | Banach J. Math. Anal. 13, no. 3 (2019), 647-674 |
| ISSN: | 1735-8787 |
| DOI: | 10.1215/17358787-2019-0015 |
| Popis: | We address questions on the existence and structure of universal functions for classes $L^{p}[0,1)^{2}$ , $p\in (0,1)$ , with respect to the double Walsh system. It is shown that there exists a measurable set $E\subset [0,1)^{2}$ with measure arbitrarily close to $1$ , such that, by a proper modification of any integrable function $f\in L^{1}[0,1)^{2}$ outside $E$ , we can get an integrable function $\tilde{f}\in L^{1}[0,1)^{2}$ , which is universal for each class $L^{p}[0,1)^{2}$ , $p\in (0,1)$ , with respect to the double Walsh system in the sense of signs of Fourier coefficients. |
| Databáze: | OpenAIRE |
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