Conference paper
Wavefront and caustic surfaces of refractive laser beam shaper
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
A recent note of Ih-Ching Hsu poses an unsolved problem, to wit, the general solution of the functional equation g(x1, x2) + g(φ1(x1), φ2(x2)) = g(x1, φ2(x2)) + g(φ1(x1),x2), where the φi are given functions. This short paper obtains the general solution. It gives conditions which imply that any continuous solution has form g1(x1) + g2(x2). © 1989 Birkhäuser Verlag.
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
A. Skumanich
SPIE OE/LASE 1992
Charles A Micchelli
Journal of Approximation Theory
I.K. Pour, D.J. Krajnovich, et al.
SPIE Optical Materials for High Average Power Lasers 1992