It is shown formally how transmutation kernels can be characterized via a minimizing procedure. The technique then can be extended to more general operators and transmutations.
REFERENCES
1.
F. Dyson, in Studies in Math. Physics (Princeton, U.P., Princeton, NJ, 1976), pp. 151–167.
2.
3.
R. Carroll, Transmutation, Scattering Theory, and Special Functions (North‐Holland, Amsterdam, 1982).
4.
5.
H. Dym and H. McKean, Gaussian Processes, Function Theory, and the Inverse Spectral Problem (Academic, New York, 1976).
6.
R. Carroll and F. Santosa, in Proceedings of the Conference on Inverse Scattering, University of Tulsa, 1983 (in press).
7.
R. Carroll and F. Santosa, “Spectral measures and autocorrelation via transmutation,” C. R. Roy. Soc. Canada (in press).
8.
9.
K. Chadan and P. Sabatier, Inverse Problems in Quantum Scattering Theory (Springer, New York, 1977).
10.
11.
V. Marcenko, Sturm‐Liouville Operators and Their Applications, (Izd. Nauk. Dumka, Kiev, 1977)—see also Ref. 3.
12.
This calculation suggests (as is indeed the case) that the characterization of by minimization does not require the trace argument [i.e., the last integral in (2.3)];
the details will appear elsewhere.
This content is only available via PDF.
© 1984 American Institute of Physics.
1984
American Institute of Physics
You do not currently have access to this content.