# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Characterization of low pass filters in a multiresolution analysis

### Tom 190 / 2009

Studia Mathematica 190 (2009), 99-116 MSC: Primary 42C40; Secondary 47B38, 42B15, 42B35, 28A33. DOI: 10.4064/sm190-2-1

#### Streszczenie

We characterize the low pass filters associated with scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by a fixed linear invertible map $A: {\mathbb R}^n\rightarrow {\mathbb R}^n$ such that $A(\mathbb Z^n) \subset \mathbb Z^n$ and all (complex) eigenvalues of $A$ have modulus greater than $1.$ This characterization involves the notion of filter multiplier of such a multiresolution analysis. Moreover, the paper contains a characterization of the measurable functions which are filter multipliers.

#### Autorzy

• A. San AntolínDepartamento de Matemáticas
Universidad Autónoma de Madrid
28049 Madrid, Spain
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek