A Szegö limit formula for conjugates of ψ DO's by Hecke operators

Steven Zelditch*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Let Tg be a Hecke operator and let Op(a) be a ψ DO on L2(Γ{minus 45 degree rule}b). Further, let πλ be the projection onto span {uj: -Δuj = λjuj, Tguj = ρ{variant}j(g) uj, √λj ≤ λ}. We will determine the Szegö limit measure μg,a for the operators Tg *Op(a) Tg: ∝-∞ xkg,a(x) = limλ → ∞ (1/rank πλ tr(πλT g * Op(a) Tgπλ)k. Comparison of μg,a with the Szegö limit measure of Op(Tga) shows that Tg * Op(a) Tg is quite remote spectrally from Op(Tga).

Original languageEnglish (US)
Pages (from-to)198-210
Number of pages13
JournalJournal of Functional Analysis
Volume77
Issue number1
DOIs
StatePublished - Jan 1 1988

ASJC Scopus subject areas

  • Analysis

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