Time-dependent deformations of powers of the wave operator
Conditions under which the linear differential operators of the second order are equivalent to operators not containing “friction” (first partial derivatives) are investigated. One can construct iso-Huygens deformations for powers of the wave operator with time-dependent coefficients. The fundamental solutions of these deformations and conditions under which the Huygens principle holds are found. Bibliography: 17 titles.
KeywordsHuygens Fundamental Solution Scalar Curvature Wave Operator Adjoint Action
Unable to display preview. Download preview PDF.
- 8.V. I. Semyanistyi, “Some problems of integral geometry in pseudo-Euclidean and non-Euclidean spaces, ” MGU, Trudy Semin. Vekt. Tenz. Anal., 13, 244–302 (1963).Google Scholar
- 9.B. Rubin, “Zeta integrals and integral geometry in the space of rectangular matrices,” Preprint, The Hebrew University, Jerusalem (2004).Google Scholar
- 10.I. M. Gel’fand, S. G. Gindikin, and M. I. Graev, Selected Problems in Integral Geometry [in Russian], Dobrosvet, Moscow (2000).Google Scholar
- 11.N. Kh. Ibragimov, Groups of Transformations in Mathematical Physics [in Russian], Fizmatgiz, Moscow (1983).Google Scholar
- 13.V. A. Zorich, Mathematical Analysis [in Russian], Vol. 2, Nauka, Moscow (1984).Google Scholar
- 14.I. M. Gel’fand and G. E. Shilov, Generalized Functions [in Russian], Vol. 1, Fizmatgiz, Moscow (1985).Google Scholar
- 15.J. F. Treves, Lectures on Linear Equations in Partial Derivatives with Constant Coefficients [Russian translation], Mir, Moscow (1965).Google Scholar
- 16.S. P. Khekalo, “Gauge related deformations of ordinary linear differential equations with constant coefficients,” Zap. Nauchn. Semin. POMI, 308, 235–251 (2004).Google Scholar