9 янв. 2022 г. · A function f:R→R is called positive definite (in the semigroup sense) if for all n≥1 and x1,…,xn∈R pairwise different the matrix (f(xi+xj))ni,j= ...

22 янв. 2024 г. · All positive definite functions on G extend to a completely positive map from the full group C∗-algebra C∗(G), so you can say φ is positive ...

27 окт. 2023 г. · A function f(x,y) is positive definite if matrices (f(xi,xj))i,j∈F are positive definite for all finite index sets F. This is frequently ...

22 авг. 2011 г. · A positive definite function φ:G→C on a group G is a function that arises as a "diagonal" coefficient of a unitary representation of G.

19 мар. 2023 г. · Positive definiteness of r(t,s) as a matrix-valued function includes symmetricity of in the sense that r⊤(t,s)=r(s,t).

25 апр. 2011 г. · Bochner's theorem states that a positive definite function is the Fourier transform of a finite Borel measure. As well, an easy converse of this ...

14 июл. 2012 г. · Bochner's theorem states that a positive definite function is the Fourier transform of a finite Borel measure.

20 июл. 2014 г. · If the matrices are real and the function you have in mind is real-valued, then you indeed get the characterization you suggested.

18 апр. 2024 г. · Strict positive definiteness is thus equivalent to ∀v∈Cn∖{0}, we have n∑i,j=1viˉvjCf(xi,xj)>0.

25 июл. 2023 г. · Here a continuous function f(x) on R≥0 is called positive definite if ∑Nk,lak¯alf(xk+xl)≥0 is satisfied for all a1,⋯,aN∈C and x1,⋯,xN∈R≥0.