Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-21T04:46:46.405Z Has data issue: false hasContentIssue false
  • English
  • Français

An application of Sturm-Liouville theory to a class of two-part boundary-value problems*

Published online by Cambridge University Press:  24 October 2008

Samuel N. Karp
Samuel N. Karp
Affiliation:
Institute of Mathematical Sciences New York University
Get access Rights & Permissions [Opens in a new window]

Abstract

A simple solution of a general problem involving a bifurcated wave guide is presented. The purpose of the work is to explain a new and simple method of solving such problems and to exhibit an organic connexion between Sturm–Liouville theory and the theory of two-part boundary-value problems.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 2 , April 1957 , pp. 368 - 381
Copyright
Copyright © Cambridge Philosophical Society 1957

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Courant, R. and Hilbert, D.Methoden der Mathematischen Physik, vol. 1 (Springer, 1931).CrossRefGoogle Scholar
(2)Grttenberg, H. and Hurd, R. A.Scattering of a plane electromagnetic vxive by an infinite stack of conducting plates. National Research Council of Canada, Radio and Electrical Engr. Div. (Ottawa, 1954).Google Scholar
(3)Ince, E. L.Ordinary differential equations (Dover, 1944).Google Scholar
(4)Kabp, S. N.Separation of variables and Wiener–Hopf techniques. Research Report no. EM-25, Mathematics Research Group (New York University, 1950).Google Scholar
(5)Karp, S. N.The natural charge distribution and capacitance of a finite conical shell, Research Report no. EM-35, Mathematics Research Group (New York University, 1951).Google Scholar
(6)Mabcttvitz, N.Waveguide handbook (McGraw Hill, 1951).Google Scholar
(7)Titchmarsh, E. C.Eigenfunction expansions (Oxford, 1946).Google Scholar
(8)Titchmarsh, E. C.The theory of functions, 2nd ed. (Oxford, 1939).Google Scholar