Equivalence between Some Orthonormal Systems
Abstract
For every orthonormal system of functions $$\{\varphi_{n}\}$$ on $$(0,\,1)$$ , pointwise bounded by a function $$f\in L^{2}(0,\,1)$$ , that is, $$|\varphi_{n}(x)|\leq f(x)$$ , it is possible to construct an orthonormal system $$\{\psi_{n}\}$$ with $$|\psi_{n}(x)|\equiv 1$$ , such that the series $$\sum a_{n}\varphi_{n}$$ and $$\sum a_{n}\psi_{n}$$ converge almost everywhere simultaneously, for every $$\{a_{n}\}\in\ell^{2}$$ .
Fields of Study & Subjects
Advanced Banach Space Theory
Advanced Harmonic Analysis Research
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)
- Volume
- 61
- Issue
- 1
- Pages
- 22–30
- Publication date
- 1 February 2026
- Language
- EN