Browsing by Issue Date, starting with "2011-03-01"
Now showing 1 - 1 of 1
Results Per Page
Sort Options
- On differentiability and analyticity of positive definite functionsPublication . Buescu, Jorge; Paixão, AntónioWe derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.