On Fejér kernels

Carathéodory-Fejér type extremal problems on locally compact Abelian groups

We consider the extremal problem of maximizing a point value | f (z) | at a given point z ∈ G by some positive definite and continuous function f on a locally compact Abelian group (LCA group) G, where for a given symmetric open set Ω ∋ z, f vanishes outside Ω and is normalized by f (0) = 1. This extremal problem was investigated in R and Rd and for Ω a 0-symmetric convex body in a paper of Boa...

Fejér Monotonicity in Convex Optimization

On Fejér Type Inequalities for (η1,η2)-Convex Functions

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (...

The Carathéodory-Fejér-Pisarenko Decomposition and Its Multivariable Counterpart

When a covariance matrix with a Toeplitz structure is written as the sum of a singular one and a positive scalar multiple of the identity, the singular summand corresponds to the covariance of a purely deterministic component of a time-series whereas the identity corresponds to white noise—this is the Carathéodory-Fejér-Pisarenko (CFP) decomposition. In the present paper we study multivariable ...

On critical kernels

We propose a method for collapsing simplicial complexes in a symmetric manner. For that purpose, we introduce the notions of a simple cell, of an essential face, and the one of a core of a cell. Then, we define the critical kernel of a complex. Our main result is that the critical kernel of a given complex X is a collapse of X. We extend this result by giving a necessary and sufficient conditio...