Inequalities and Positive-Definite Functions Arising from a Problem in Multidimensional Scaling

Some numerical radius inequalities with positive definite functions

 ‎Using several examples of positive definite functions‎, ‎some inequalities for the numerical radius of‎ ‎matrices are investigated‎. ‎Also‎, ‎some open problems are stated‎.

some numerical radius inequalities with positive definite functions

‎using several examples of positive definite functions‎, ‎some inequalities for the numerical radius of‎ ‎matrices are investigated‎. ‎also‎, ‎some open problems are stated‎.

Schoenberg’s Problem on Positive Definite Functions

Positive Definite Functions and Multidimensional Versions of Random Variables

aiXi and γ(a)Y are identically distributed, where γ : R → [0,∞) is called the standard of X. An old problem is to characterize those functions γ that can appear as the standard of an n-dimensional version. In this paper, we prove the conjecture of Lisitsky that every standard must be the norm of a space that embeds in L0. This result is almost optimal, as the norm of any finite dimensional subs...

On a Problem of Turán about Positive Definite Functions

We study the following question posed by Turán. Suppose Ω is a convex body in Euclidean space Rd which is symmetric in Ω and with value 1 at the origin; which one has the largest integral? It is probably the case that the extremal function is the indicator of the half-body convolved with itself and properly scaled, but this has been proved only for a small class of domains so far. We add to thi...