Wave operators for pairs of spaces and the Klein-Gordon equation

Aequationes mathematicae - Tập 20 - Trang 38-50 - 1980
Martin Schechter1
1Belfer Graduate School of Science, Yeshiva University, New York, U.S.A.

Tóm tắt

We give a new criterion for the existence of wave operators for pairs of self adjoint operators acting in different Hilbert spaces. We apply this method to obtain results for the Klein-Gordon equation.

Tài liệu tham khảo

Cook, J. M. Convergence to the Møller wave-matrix. J. Math. Phys.36 (1957), 82–87. Jauch, J. M. Theory of the scattering operator. Helv. Phys. Acta31 (1958), 127–158. Kuroda, S. T.,On the existence and unitary property of the scattering operator. Nuovo Cimento12 (1959), 431–454. Kato, Tosio,Perturbation theory for linear operators. Springer, Berlin, 1966. Prosser, R. T.,Relativistic potential scattering. J. Mathematical Phys.4 (1963), 1048–1054. Eckardt, K.-J.,On the existence of wave operators for Dirac operators. Manuscripta Math.11 (1974), 359–371. Schechter, Martin,Scattering theory for elliptic operators of arbitrary order. Comment. Math. Helv.49 (1974), 84–113. Schechter, Martin,Nonhomogeneous elliptic systems and scattering. Tohoku Math. J.27 (1975), 601–616. Schechter, Martin,Spectra of partial differential operators. North-Holland, Amsterdam, 1971. Schiff, L. I.,Quantum mechanics. McGraw-Hill, New York, 1968. Veselic, Kresimir andWeidmann, Joachim,Asymptotic estimates of wave functions and the existence of wave operators. J. Functional analysis17 (1974), 61–77. Eckardt, E.-J.,On the existence of wave operators for the Klein-Gordon equation. To appear. Schechter, Martin,The Klein-Gordon equation and scattering theory. Ann. Physics,101 (1976), 601–609. Lundberg, L.-E.,Spectral and scattering theory for the Klein-Gordon equation. Commun. Math. Phys.31 (1973), 243–257. Thoe, D.,Spectral theory for the wave equation with a potential term. Arch. Rational Mech. Anal.22 (1966), 364–406. Strauss, W. A.,Scattering for hyperbolic equations. Trans. Amer. Math. Soc.108 (1963), 13–37. Weder, R. A.,Scattering theory for the Klein-Gordon equation. To appear. Eckardt, K.-J.,Scattering theory for the Klein-Gordon equation. To appear. Schechter, Martin,A new criterion for scattering theory. To appear. Simon, B.,Scattering theory and quadratic forms: On a theory of Schechter. Commun. Math. Phys.53 (1977), 151–153. Kato, Tosio,Scattering theory with two Hilbert spaces. J. Functional Analysis1 (1967), 342–369.