Positive defined functions on the line, some representation results and examples
Abstract
The representation results for positive definite functions on the real line given by S. Bochner, F. Riez and M. Crum are stated. In self-contained way, some results about positive definite functions in abelian groups and functional equations are proved. These results are used to:
(ii) Give non trivial examples of positive defined functions on the real line which are null at almost every point.
(ii) Give examples of positive definite functions on the real line with infinite points of discontinuity.
(iii) Show that there exits non measurable positive definite functions on the real line.
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References
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