REPRESENTATION OF FUNCTIONS BY ORTHOGONAL SERIES.
Abstract
The author proves the following theorem on the basis of a direct construction of the functions (phi sub n)(x). Let summation from n=1 to n=infinity of ((a sub n)squared)= + infinity and let F(x) be an arbitrary measurable function, with extended real values, on (0,1). Then there exists an orthonormal system (phi sub n)(x) with the property that each rearrangement of the series summation of ((a sub n)(phi sub n)(x)) converges almost everywhere to F(x). (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 31, 1969
- Accession Number
- AD0700419
Entities
People
- R. I. Osipov
Organizations
- Johns Hopkins University Applied Physics Laboratory