Construction of Continuous Frames in Hilbert spaces

TL;DR

This paper explores the construction of continuous frames in Hilbert spaces, demonstrating conditions under which they can be formed and providing illustrative examples.

Contribution

It introduces new conditions for constructing continuous frames in Hilbert spaces and offers explicit examples demonstrating these constructions.

Findings

Continuous frames can be constructed under specific measure and dimension conditions.

The paper provides explicit examples of continuous frames.

Conditions for the existence of continuous frames are established.

Abstract

Extending the concept of frame to continuous frame, in this manuscript we will show that under certain conditions on the measure of $\Omega$ and the dimension of $\h$ we can construct continuous frames. Also, some examples are given.