intersection of positive and positive definite cones?

Stream: maths

[Nicholas Wilson]

More of a literature question: Is there a specific name for the function cone that is the intersection of the cone of positive functions and the cone of positive definite functions on a given space?

[Yaël Dillies]

What do you mean by positive functions and positive definite functions here?

[Nicholas Wilson]

respectively f(x) : ∀ f(x) ≥ 0 (and f is not the zero function), https://en.wikipedia.org/wiki/Positive-definite_function definition 1

[Eric Wieser]

The first is 0 < f in mathlib, I think

[Nicholas Wilson]

The definitions are not hard (Positive definite functions are Fourier transforms of positive functions), I just wondered if their intersection of those function cones has a specific name. Both for a literature search to see if there is anything interesting that might apply, but also so that I can use a name consistent with what it already in use (if such a name exists).

[Yaël Dillies]

The term I know for positive-definite functions is "nonnegative in Fourier space"

[Yaël Dillies]

Never heard of a name for the intersection

[Anatole Dedecker]

And the name I know is "functions of positive type"