The eigenvalues of the Laplacian on a sphere with boundary conditions specified on a segment of a great circle

Journal of Mathematical Physics

Volumn 38, Issue 3, 1997, Pages 1623-1649

  Abawi, Ahmad T ^a,b   Dashen, Roger F ^a   Levine, Herbert ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b AETC Incorporated   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031506709     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531820     Document Type: Article

References (14)

1. L. Kraus and L. Levine, "Diffraction by an elliptic cone," Commun. Pure Appl. Math. 9, 49-68 (1961).
2. J. Radlow, "Diffraction by a quarter plane," Arch. Rational Mech. Anal. 8, 139-158 (1961).
3. V. S. Blume and M. Kirchner, "Das beugungsnahfeld an der spitze eines sektorformigen schlizes in einem ebenen schirn," Inst. Angewandte Phys. Univ. Marburg, 29, 185-203 (1968).
4. R. Satterwhite, "Diffraction by a Plane Angular Sector," Ph.D. thesis, Ohio State University, 1969.
5. R. De Smedt and J. G. Van Bladel, "Field singularities at the tip of a metallic cone of arbitrary cross section," IEEE Trans. Antennas Propag. AP-34, 865-870 (1986).
6. J. Boersma, "Singularity exponents for complementary sectors," Electron. Lett. 27, 1484-1485 (1991).
7. J. Mathews and R. L. Walker, Mathematical Methods of Physics, 2nd ed. (Addison-Wesley, Reading, MA, 1970).
8. E. Ince, "Further investigations into the periodic Lamé functions," Proc. R. Soc. Edinburgh A 60, 87-99 (1940).
9. F. W. J. Olver, Asymptotics and Special Functions (Academic, New York, 1974).
10. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
11. A. T. Abawi, "The WKB Solution of the Wave Equation for a Plane Angular Sector," Ph.D. thesis, University of California, San Diego, 1993.
12. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 2nd ed. (Academic, New York, 1980).
13. P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists (Springer-Verlag, Berlin, 1954).
14. W. H. Press, Numerical Recipes, 2nd ed. (Cambridge University Press, Cambridge, 1992).