Abstract
Let μ be a Borel probability measure with compact support in R2. μ is called a spectral measure if there exists a countable set Λ⊂R2 such that EΛ={e−2πi〈λ,x〉:λ∈Λ} is an orthonormal basis for L2(μ). In this note we prove that the integral Sierpinski measure μA,D is a spectral measure if and only if (A,D) is admissible. This completely settles the spectrality of integral Sierpinski measures in R2.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.