Filters and Functions in Multi-scale Constructions: Extended Abstract
Wayne M. Lawton
TL;DR
This paper investigates the geometric means of Fourier moduli in multi-scale constructions, focusing on refinable distributions with arbitrary dilations and translations, especially using Pisot-Vijayaraghavan numbers.
Contribution
It introduces new results on Fourier modulus geometric means and develops multi-scale constructions for specific algebraic dilations and translations in quasilattices.
Findings
Derived formulas for Fourier modulus geometric means.
Established multi-scale construction methods for Pisot-Vijayaraghavan dilations.
Extended theoretical understanding of refinable distributions.
Abstract
We derive results about geometric means of the Fourier modulus of filters and functions related to refinable distributions with arbitrary dilations and translations. Then we develop multi-scale constructions for dilations by Pisot-Vijayaraghavan numbers and translations in associated quasilattices.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical Dynamics and Fractals · Mathematical Analysis and Transform Methods