On Translation Invariant Kernels and Screw FunctionsReport as inadecuate



 On Translation Invariant Kernels and Screw Functions


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We explore the connection between Hilbertian metrics and positive definite kernels on the real line. In particular, we look at a well-known characterization of translation invariant Hilbertian metrics on the real line by von Neumann and Schoenberg 1941. Using this result we are able to give an alternate proof of Bochners theorem for translation invariant positive definite kernels on the real line Rudin, 1962.



Author: Purushottam Kar; Harish Karnick

Source: https://archive.org/







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