Abstract
AbstractThe self‐affine measure corresponding to an expanding matrix and the digit set in the space is supported on the spatial Sierpinski gasket, where are the standard basis of unit column vectors in and . In the case and , it is conjectured that the cardinality of orthogonal exponentials in the Hilbert space is at most “4”, where the number 4 is the best upper bound. That is, all the four‐element sets of orthogonal exponentials are maximal. This conjecture has been proved to be false by giving a class of the five‐element orthogonal exponentials in . In the present paper, we construct a class of the eight‐element orthogonal exponentials in the corresponding Hilbert space to disprove the conjecture. We also illustrate that the constructed sets of orthogonal exponentials are maximal.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
