Bernau Spline Wavelets and Sturmian Sequences

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F04%3A00105294" target="_blank" >RIV/68407700:21340/04:00105294 - isvavai.cz</a>

Result on the web

—

DOI - Digital Object Identifier

—

Result language

angličtina

Original language name

Bernau Spline Wavelets and Sturmian Sequences

Original language description

We present spline wavelets of class C-n (R) supported by sequences of aperiodic discretizations of R. The construction is based on multiresolution analysis recently elaborated by G. Bernuau. At a given scale, we consider discretizations that are sets ofleft-hand ends of tiles in a self-similar tiling of the real line with finite local complexity. Corresponding tilings are determined by two-letter Sturmian substitution sequences. We illustrate the construction with examples having quadratic Pisot-Vijayaragha van units (like tau = (1 + root5)/2 or tau(2) = (3 + root6)/2) as scaling factor. In particular, we present a comprehensive analysis of the Fibonacci chain and give the analytic form of related scaling functions and wavelets. We also give some hints for the construction of multidimensional spline wavelets based on stone-inflation tilings in arbitrary dimension.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BE - Theoretical physics

OECD FORD branch

—

Project

—

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2004

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

The Journal of Fourier Analysis and Application

ISSN

1069-5869

e-ISSN

—

Volume of the periodical

10

Issue of the periodical within the volume

3

Country of publishing house

US - UNITED STATES

Number of pages

32

Pages from-to

—

UT code for WoS article

000222115300005

EID of the result in the Scopus database

—