Spectrality of the planar Sierpinski family

Autor:	Xing-Gang He, Li-Xiang An, Li Tao
Rok vydání:	2015
Předmět:	Combinatorics Discrete mathematics Planar Applied Mathematics Countable set Orthonormal basis Borel probability measure σ-finite measure Measure (mathematics) Spectral measure Analysis Mathematics Sierpinski triangle
Zdroj:	Journal of Mathematical Analysis and Applications. 432:725-732
ISSN:	0022-247X
DOI:	10.1016/j.jmaa.2015.06.064
Popis:	Let μ be a Borel probability measure with compact support in R 2 . μ is called a spectral measure if there exists a countable set Λ ⊂ R 2 such that E Λ = { e − 2 π i 〈 λ , x 〉 : λ ∈ Λ } is an orthonormal basis for L 2 ( μ ) . In this note we prove that the integral Sierpinski measure μ A , D is a spectral measure if and only if ( A , D ) is admissible. This completely settles the spectrality of integral Sierpinski measures in R 2 .
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::114d13d3cfdab23e18992c74cc2b2c27 https://doi.org/10.1016/j.jmaa.2015.06.064 Zobrazit plný text záznamu Full Text from ScienceDirect