Characterization of low pass filters in a multiresolution analysis

• Autorzy: A. San Antolín
• Języki publikacji: EN

Abstrakty

EN

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: ℝⁿ → ℝⁿ such that A(ℤⁿ) ⊂ ℤⁿ 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.

Kategorie tematyczne

• 42B15: Multipliers
• 42B35: Function spaces arising in harmonic analysis
• 42C40: Wavelets and other special systems
• 47B38: Operators on function spaces (general)
• 28A33: Spaces of measures, convergence of measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 190
• Numer: 2
• Strony: 99-116

Daty

wydano

2009

Twórcy

autor

A. San Antolín

• Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Identyfikatory

DOI

10.4064/sm190-2-1