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- W2315754948 abstract "Let G be an abelian group, written additively. A complexvalued function ƒ, defined on G, is said to be positive definite if the inequality 1 holds for every choice of complex numbers C 1 , …, c n and S 1 , …, s n in G. It follows directly from (1) that every positive definite function is bounded. Weil ( 9 , p. 122) and Raïkov ( 5 ) proved that every continuous positive definite function on a locally compact abelian group is the Fourier-Stieltjes transform of a bounded positive measure, thus generalizing theorems of Herglotz ( 4 ) ( G = Z , the integers) and Bochner ( 1 ) (G = R, the real numbers). If ƒ is a continuous function, then condition ( 1 ) is equivalent to the condition that 2" @default.
- W2315754948 created "2016-06-24" @default.
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- W2315754948 date "1969-01-01" @default.
- W2315754948 modified "2023-09-27" @default.
- W2315754948 title "Unbounded Positive Definite Functions" @default.
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- W2315754948 doi "https://doi.org/10.4153/cjm-1969-143-4" @default.
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