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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
Affiliation:
Institute of Mathematical Sciences New York University

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
Copyright
Copyright © Cambridge Philosophical Society 1957

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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