Abstract
It is shown that the solution space of a system of discrete Wiener-Hopf equations is a set of points on an infinite-dimensional Grassmann manifold. Fractional transformations acting on the solution space are also discussed.
Similar content being viewed by others
References
SatoM., RIMS Kôkyûroku, Kyoto Univ. 439, 30–46 (1981); Sato, M. and Sato, Y., in H. Fujita, P. D. Lax, and G. Strang (eds.), Nonlinear Partial Differential Equations in Applied Science; Proceedings of the U.S.-Japan Seminar, Tokyo, 1982, North-Holland, Amsterdam, 1983.
DateE., KashiwaraM., JimboM., and MiwaT., in M.Jimbo and T.Miwa (eds.), Non-linear Integrable System-Classical Theory and Quantum Theory, World Scientifić, Singapore, 1983.
UenoK., in V.Kac (ed.), Infinite Dimensional Groups with Applications, Springer, New York, 1985.
SegalG. and WilsonG., Publ. Math. I.H.E.S. 61, 5–65 (1985).
TakasakiK., Commun. Math. Phys. 94, 35–59 (1984); Saitama Math. J. 3, 11–40 (1985).
NakamuraY., J. Math. Phys. 29, 244–248 (1988).
SpeckF.-D., General Wiener-Hopf Factorization Methods, Pitman, Boston, 1985.
HochstadtH., Integral Equations, Wiley, New York, 1973.
Takasaki, K., Geometry of universal Grassmann manifold-Line bundle, connection, and curvature, preprint, Kyoto Univ., 1988.
Nakamura, Y., Riemann-Hilbert transformations for a Toepliz matrix equation: Some ideas and applications to linear prediction problem, preprint, Gifu Univ., 1987.
KailathT., IEEE Trans. Information Theory IT-15, 665–672 (1969).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nakamura, Y. Solution space of discrete Wiener-Hopf equations and Grassmann manifold. Lett Math Phys 16, 273–277 (1988). https://doi.org/10.1007/BF00398965
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00398965