Two-dimensional, highly directive currents on large circular loops

Journal of Mathematical Physics

Volumn 41, Issue 9, 2000, Pages 6130-6172

  Margetis, Dionisios ^a   Fikioris, George ^b  

^a HARVARD UNIVERSITY   (United States)

^b NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034344615     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1288245     Document Type: Article

References (26)

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5. T. S. Angell and A. Kirsch, Math. Methods Appl. Sci. 15, 647 (1992); T. S. Angell, R. E. Kleinman, and B. Vainberg, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 59, 242 (1998).
6. G. Fikioris, Ph.D. thesis, Harvard University, 1993.
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8. Various issues of routine rigor such as the interpretation of the Laplacian, the nature of the limit at the boundary, and the admissible data h(s) are not addressed in this paper. It is sufficient although not necessary to state that C is a simple closed, rectifiable, and infinitely differentiable curve.
9. c without lying in C.
10. 2 is assumed to exist and be finite.
11. A finite-dimensional version of the present problem involves the maximization of a linear function over the intersection of a sphere and an ellipsoid. Accordingly, no complication of any kind should arise in the use of the Lagrange multipliers.
12. Bateman Manuscript Project, Higher Transcendental Functions, edited by A. Erdélyi (Krieger, Malabar, FL, 1981), Vol. II, pp. 80, 81, 85, 86, 87, 96, 102, 317.
13. For the statement of a theorem underlying the Poisson summation formula see T. M. Apostol, Mathematical Analysis (Addison-Wesley, Reading, MA, 1974), pp. 332-335.
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15. R. J. Sasiela and J. D. Shelton, J. Math. Phys. 34, 2572 (1993).
16. Of course, the logarithmic derivative φ(z) of the gamma function here should not be confused with the φ(r̂) of Eq. (2.4).
17. B. J. Stoyanov and R. A. Farrell, Math. Comput. 49, 275 (1987). These authors calculate only the first three terms of the asymptotic expansion (3.30). Their method does not make use of the Mellin transform technique.
18. Bateman Manuscript Project, Higher Transcendental Functions, edited by A. Erdélyi (Krieger, Malabar, FL, 1981), Vol, I, pp. 101, 182, 267.
19. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1972), pp. 365-367, 446.
20. D. Margetis, Chap. 5 of Ph.D. thesis, Harvard University, 1999.
21. C. W. Oseen, Ann. Phys. (Leipzig) 69, 202 (1922).
22. α→0 of its right-hand side are not equal.
23. For a fixed point in C and a fixed number of reflections, the contributing rays can result from minimizing the total length of all possible paths that originate from a line of reference, by running parallel or antiparallel to the direction of maximum field.
24. G. N. Watson, Proc. R. Soc. London, Ser. A 95, 83 (1918).
25. N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space (Dover, New York, 1993), Vol. I, pp. 74-77.
26. E. C. Titchmarsh. Introduction to the Theory of Fourier Integrals (Chelsea, New York, 1986), p. 69.