6533b7cffe1ef96bd1258749

RESEARCH PRODUCT

Some analytical considerations on two-scale relations

Fabio BagarelloFabio BagarelloJean-pierre Antoine

subject

PhysicsMathematics::Functional AnalysisScale (ratio)mathematical methods in physicsFixed pointIntegerProbability theoryOrthogonalityPosition (vector)Computer Science::Computer Vision and Pattern RecognitionQuantum mechanicsApplied mathematicsSettore MAT/07 - Fisica MatematicaScalingEigenvalues and eigenvectors

description

Scaling functions that generate a multiresolution analysis (MRA) satisfy, among other conditions, the so-called «two-scale relation» (TSR). In this paper we discuss a number of properties that follow from the TSR alone, independently of any MRA: position of zeros (mainly for continuous scaling functions), existence theorems (using fixed point and eigenvalue arguments) and orthogonality relation between integer translates. © 1994 Società Italiana di Fisica.

yearjournalcountryeditionlanguage
1994-08-01Il Nuovo Cimento B
https://doi.org/10.1007/bf02722465