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Three‐Dimensional Fourier Transforms and Their Application to Maxwell's Equations
1.J. L. Barnes and M. F. Gardner, Transients in Linear Systems (John Wiley and Sons, Inc., New York, 1942).
2.E. U. Condon, Rev. Mod. Phys. 14, 341–89 (1942).
3.The above assumptions are obviously fulfilled by the electric and magnetic field strengths and in the following we shall always assume that the functions considered satisfy these conditions.
4.Cf. R. V. Churchill, Modern Operational Mathematics in Engineering (McGraw‐Hill Book Company, Inc., New York, 1944), Chap. X;
4.and G. Doetsch, Math. Ann. 112, 52 (1936);
4.H. Kniess, Math. Zeits. 44, 266 (1939).
5.J. W. Gibbs and E. B. Wilson, Vector Analysis (Yale University Press, New Haven, 1922), p. 409.
6.The appearance of these spurious boundary values of the function which are not given by the problem is considered by Doetsch (reference 3).
7.(10) and (11) are the transforms of the equations giving E and H in terms of the vector potential A and the scalar potential φ and hold quite generally, since we have not yet used the fact that div
8.E. U. Condon, reference 2, p. 348.
9. is defined to be equal to one for and zero otherwise.
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