On the Dini calculus. II
type: Item
instance of: scholarly article
title: On the Dini calculus. II
zbMATH Open document ID: 0715.42020
DOI: 10.1016/0022-247X(89)90244-8
author: M. Scott Osborne
author: Garth Warner
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: In an earlier note (Part I) in this Journal 118, 255-262 (1986; Zbl 0606.42012), we introduced the notion of the Dini calculus and developed it completely in the 1-dimensional case. At the end of that article, we offered a conjecture on how things should go in general. Our purpose here will be to confirm that conjecture. In essence, the main theme is the abstract Dini theorem. It is a theorem of existence, thus it is qualitative in nature. We have also included a vanishing theorem that provides the justification for a claim made elsewhere by us [Pac. J. Math. 140, No.2, 263-352 (1989; Zbl 0697.22021), Section 10]. While of independent interest, the main immediate application of these results is to the derivation of the Selberg trace formula [the authors, Trans. Am. Math. Soc. 324, No.2, 623-653 (1991)].
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 42C20
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 11F72
zbMATH DE Number: 4177839
zbMATH Keywords: Dini integral
zbMATH Keywords: Paley-Wiener space
zbMATH Keywords: Dini calculus
zbMATH Keywords: abstract Dini theorem
zbMATH Keywords: Selberg trace formula
MaRDI profile type: Publication
cites work: On the Dini calculus
cites work: The Selberg trace formula. VII: Application of the truncation process to the continuous spectrum
cites work: The Selberg Trace Formula. VIII, Contribution from the Continuous Spectrum
description: scientific article; zbMATH DE number 4177839