There are eight‐element orthogonal exponentials on the spatial Sierpinski gasket

Qi Wang and Jian‐Lin Li

Mathematische Nachrichten, 2019, vol. 292, issue 1, 211-226

Abstract: The self‐affine measure μM,D corresponding to an expanding matrix M=diag[p1,p2,p3] and the digit set D=0,e1,e2,e3 in the space R3 is supported on the spatial Sierpinski gasket, where e1,e2,e3 are the standard basis of unit column vectors in R3 and p1,p2,p3∈Z∖{0,±1}. In the case p1∈2Z and p2,p3∈2Z+1, it is conjectured that the cardinality of orthogonal exponentials in the Hilbert space L2(μM,D) 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 L2(μM,D). In the present paper, we construct a class of the eight‐element orthogonal exponentials in the corresponding Hilbert space L2(μM,D) to disprove the conjecture. We also illustrate that the constructed sets of orthogonal exponentials are maximal.

Date: 2019
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.201700471

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:292:y:2019:i:1:p:211-226

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().