Charles Sturm and the Development of Sturm-Liouville Theory in the Years 1900 to 1950

W. Norrie Everitt ()
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W. Norrie Everitt: University of Birmingham Edgbaston, School of Mathematics and Statistics

A chapter in Sturm-Liouville Theory, 2005, pp 45-74 from Springer

Abstract: Abstract The first joint publication by Sturm and Liouville in 1837 introduced the general theory of Sturm-Liouville differential equations. This present paper is concerned with the remarkable development in the theory of Sturm-Liouville boundary value problems, which took place during the years from 1900 to 1950. Whilst many mathematicians contributed to Sturm-Liouville theory in this period, this manuscript is concerned with the early work of Sturm and Liouville (1837) and then the contributions of Hermann Weyl (1910), A.C. Dixon (1912), M.H. Stone (1932) and E.C. Titchmarsh (1940 to 1950). The results of Weyl and Titchmarsh are essentially derived within classical, real and complex mathematical analysis. The results of Stone apply to examples of self-adjoint operators in the abstract theory of Hilbert spaces and in the theory of ordinary linear differential equations. In addition to giving some details of these varied contributions an attempt is made to show the interaction between these two different methods of studying Sturm-Liouville theory.

Keywords: Sturm-Liouville; ordinary linear differential equations; history of mathematics (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7359-7_3

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DOI: 10.1007/3-7643-7359-8_3

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