PIP-Space Valued Reproducing Pairs of Measurable Functions

Reproducing Pairs of Measurable Functions and Partial Inner Product Spaces

We continue the analysis of reproducing pairs of weakly measurable functions, which generalize continuous frames. More precisely, we examine the case where the defining measurable functions take their values in a partial inner product space (PIP spaces). Several examples, both discrete and continuous, are presented.

On Spaces of Measurable Vector - Valued Functions 399 Proof

Complex Valued Functions Space

We adopt the following convention: x1, x2, z are sets, A is a non empty set, and f , g, h are elements of CA. Let us consider A. The functor +CA yielding a binary operation on CA is defined by: (Def. 1) For all elements f , g of CA holds +CA(f, g) = (+C)◦(f, g). Let us consider A. The functor ·CA yielding a binary operation on CA is defined as follows: (Def. 2) For all elements f , g of CA hold...

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

Dual Szegö pairs of sequences of rational matrix-valued functions

We study certain sequences of rational matrix-valued functions with poles outside the unit circle. These sequences are recursively constructed based on a sequence of complex numbers with norm less than one and a sequence of strictly contractive matrices. We present some basic facts on the rational matrix-valued functions belonging to such kind of sequences and we will see that the validity of s...