# Univariate tight wavelet frames of minimal support

## TL;DR

This paper characterizes all minimal-support tight wavelet frames for L^2(R) with a fixed number of generators using spectral techniques and Hardy space operator-valued functions, fully solving cases with one and two generators.

## Contribution

It provides a complete spectral characterization of minimal-support tight wavelet frames for one and two generators, advancing the understanding of wavelet frame construction.

## Key findings

- Complete solutions for one and two generator cases
- Spectral formulas characterize all minimal-support tight wavelet frames
- Association with Hardy space operator-valued functions

## Abstract

Wavelet frames for $L^2({\mathbb R})$ can be characterized by means of spectral techniques. This work uses spectral formulas to determine all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed finite number of generators of minimal support. The method associates wavelet frames of this type with certain inner operator-valued functions in Hardy spaces. The cases with one and two generators are completely solved.