Re: positive definite functions

In article <soj6f119lvfg6h7mqg2q4fdmnsei2k1aq8@xxxxxxx>,
David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx> wrote:


>
> Anyway, the interesting thing here is Bochner's theorem: A function
> on R is the Fourier transform of a Borel probability measure _if and
> only if_ it's continuous, positive definite and equals 1 at the
> origin. (Similarly in more general settings, for example locally
> compact abelian groups at least.)
>


Now what my question was meant to be: are there ways to verify (at least
for some classes of functions) if a function is positive definite,
without calculation of its Fourier transform or of the determinants in
the definition of positive-definiteness, as both in general are
prohibitively complicated?

Thanks,
John.
.

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