SPECTRALITY AND NON-SPECTRALITY OF PLANAR SELF-SIMILAR MEASURES WITH FOUR-ELEMENT DIGIT SETS
| Autor: | Min-Wei Tang, Si Chen |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
010102 general mathematics Spectrum (functional analysis) 01 natural sciences Measure (mathematics) Sierpinski triangle Combinatorics Matrix (mathematics) TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Planar Iterated function system Modeling and Simulation 0103 physical sciences ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Hausdorff measure 010307 mathematical physics Geometry and Topology 0101 mathematics Unit (ring theory) ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Fractals. 28:2050130 |
| ISSN: | 1793-6543 0218-348X |
| DOI: | 10.1142/s0218348x20501303 |
| Popis: | Let [Formula: see text] be the unit matrix and [Formula: see text]. In this paper, we consider the self-similar measure [Formula: see text] on [Formula: see text] generated by the iterated function system [Formula: see text] where [Formula: see text]. We prove that there exists [Formula: see text] such that [Formula: see text] is an orthonormal basis for [Formula: see text] if and only if [Formula: see text] for some integer [Formula: see text]. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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