Principal distributions for almost unperturbed Schrödinger pairs of operators

Xia, Daoxing

doi:10.1090/S0002-9939-1991-1042275-9

Principal distributions for almost unperturbed Schrödinger pairs of operators
HTML articles powered by AMS MathViewer

by Daoxing Xia

Proc. Amer. Math. Soc. 112 (1991), 745-754

DOI: https://doi.org/10.1090/S0002-9939-1991-1042275-9

PDF | Request permission

Abstract:

The relation between the principal distribution for an almost unperturbed Schrödinger pair operators $\{ U,V\}$ and the unitary operator $W$ satisfying $V = {W^{ - 1}}UW$ is found.

References

M. Š. Birman, Existence conditions for wave operators, Izv. Akad. Nauk SSSR Ser. Mat. 27 (1963), 883–906 (Russian). MR 0161150
Richard W. Carey and Joel D. Pincus, Mosaics, principal functions, and mean motion in von Neumann algebras, Acta Math. 138 (1977), no. 3-4, 153–218. MR 435901, DOI 10.1007/BF02392315
Richard W. Carey and Joel D. Pincus, Almost commuting pairs of unitary operators and flat currents, Integral Equations Operator Theory 4 (1981), no. 1, 45–122. MR 602619, DOI 10.1007/BF01682746
Louis de Branges, Perturbations of self-adjoint transformations, Amer. J. Math. 84 (1962), 543–560. MR 154132, DOI 10.2307/2372861
Shige Toshi Kuroda, Perturbation of continuous spectra by unbounded operators. II, J. Math. Soc. Japan 12 (1960), 243–257. MR 140947, DOI 10.2969/jmsj/01230243
Michael Reed and Barry Simon, Methods of modern mathematical physics. III, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. Scattering theory. MR 529429
Daoxing Xia, On the almost unperturbed Schrödinger pair of operators, Integral Equations Operator Theory 12 (1989), no. 2, 241–279. MR 986597, DOI 10.1007/BF01195116