Brown, Brian Malcolm, Eastham, M. S. P. and Evans, William Desmond 2004. Laudatum. Journal of computational and applied mathematics 171 (1-2) , xi-xiii. 10.1016/j.cam.2004.01.034 |
Abstract
This work naturally led on to the now familiar deficiency index problem [11] where, at an early stage, Norrie drew attention to the developments in Russia by making available the English edition of Naimark's book on linear differential operators. As a refinement of this problem, Norrie identified the concepts of the strong limit-n classification and separation [6] and [13]. In a further seminal paper [8], Norrie initiated the study of the asymptotic form of the Titchmarsh–Weyl m(λ) function for large |λ|. During the following 30 years, this paper has led to many fruitful and attractive papers which are now being celebrated in the Cardiff meeting of 2004. The long-standing Hardy, Littlewood, Polya inequality relates the norms of a function and its first two derivatives. Norrie's 1972 paper [10] placed this inequality in a new spectral setting which has spawned a large class of HELP inequalities, where the E for Everitt is now included in his honour. This work continued with, amongst others, the incisive papers [2], [12] and [3] together with contributions from many fellow researchers. Norrie has for many years been interested in the spectral theory of orthogonal polynomials and connections with higher order equations and Sobolev orthogonality. He has explored the spectral theory of these problems under both the so called right- and left-definite hypotheses (see for example [14]). Norrie has always been interested in exploring new approaches to his mathematics and was instrumental (with Zettl and Bailey) in setting up the SLEIGN2 programme which resulted in a computer code to calculate the eigenvalues of the Sturm–Liouville problem under a wide range of assumptions which include the limit-point, limit-circle cases and also the periodic problem (see for example [1]). This code is in wide use today both by mathematicians and scientists who need to explore the eigenvalue structure of their problem. These remarks are only a partial appreciation of Norrie's wide-ranging research in spectral theory, but the papers in the present volume are a testimony to the esteem with which his work is held by his many friends and colleagues
Item Type: | Article |
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Date Type: | Publication |
Status: | Published |
Schools: | Computer Science & Informatics |
Subjects: | Q Science > QA Mathematics > QA76 Computer software |
Publisher: | E |
ISSN: | 0377-0427 |
Last Modified: | 04 Jun 2017 04:42 |
URI: | http://orca.cardiff.ac.uk/id/eprint/43333 |
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