Surgery of spline-type and molecular frames

TL;DR

This paper introduces a method for constructing new frames in spline-type spaces by combining existing frames, with applications to time-frequency analysis and sampling in integral transforms.

Contribution

It presents a novel approach to generate frames for spline-type spaces by assembling parts of known frames, extending their applicability.

Findings

New frames can be constructed for spline-type spaces by combining existing frames.

Applications demonstrated in time-frequency decompositions.

Results applicable to sampling theory in integral transforms.

Abstract

We prove a result about producing new frames for general spline-type spaces by piecing together portions of known frames. Using spline-type spaces as models for the range of certain integral transforms, we obtain results for time-frequency decompositions and sampling.