2022/05/07 by Zheng, Ya-Li, Ai, Wen-Hui
#46C05 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 28A80 #Secondary 42C05
paper · doi:10.48550/arxiv.2205.03541
Let ρ=((p)/(q))(1)/(r)<1 for some p,q,r∈ℕ with (p,q)=1 and Dn=\0,1,⋅⋅⋅,Nn-1\, where Nn is prime for all n∈ℕ, and denote M=sup\Nn:n=1,2,3,…\1. Contrastly, if (q,Nn)=1 and (p,Nn)=1 for all n∈ℕ, then there are at most M mutually orthogonal exponential functions in L2(μ_ρ, \Dn\) and M is the best possible. If (q,Nn)=1 and (p,Nn)>1 for all n∈ℕ, then there are any number of orthogonal exponential functions in L2(μ_ρ, \Dn\).