Premium
Duality relation on spectra of self‐affine measures
Author(s) -
Li JianLin
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600192
Subject(s) - duality (order theory) , affine transformation , conjecture , mathematics , pure mathematics , property (philosophy) , spectral line , relation (database) , measure (data warehouse) , physics , quantum mechanics , computer science , philosophy , epistemology , database
The present paper establishes a duality relation for the spectra of self‐affine measures. This is done under the condition of compatible pair and is motivated by a duality conjecture of Dutkay and Jorgensen on the spectrality of self‐affine measures. For the spectral self‐affine measure, we first obtain a structural property of spectra which indicates that one can get new spectra from old ones. We then establish a duality property for the spectra which confirms the conjecture in a certain case.