Abstract
1. The main purpose of this paper is to prove some theorems about conjugate Fourier series, and similar orthogonal expansions, of a positive definite function. At the end of the paper there is given a slight generalization of the well-known continuity theorem for characteristic functions. It was proved several years ago by Dugue [1 ] that if X is a measurable positive-definite function then the Fourier series of 4) is uniformly convergent. Dugue's Theorem was actually stated in terms of characteristic functions, but it is equivalent to the present formulation on account of the Bochner-Khintchine Representation Theorem. More precisely one can state:
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
