Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Wave operators and similarity for generators of semigroups in Banach spaces


Author: Sue-chin Lin
Journal: Trans. Amer. Math. Soc. 139 (1969), 469-494
MSC: Primary 47.48
DOI: https://doi.org/10.1090/S0002-9947-1969-0240667-1
MathSciNet review: 0240667
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] K. O. Friedrichs, Über die Spektralzerlegung eines Integral-operators, Math. Ann. 115 (1938), 259-272.
  • [2] -, On the perturbation of continuous spectra, Comm. Pure Appl. Math. 1 (1948), 361-406. MR 0029100 (10:547e)
  • [3] M. Rosenblum, Perturbation of the continuous spectrum and unitary equivalence, Pacific J. Math. 7 (1957), 997-1010. MR 0090028 (19:756i)
  • [4] T. Kato, On finite-dimensional perturbations of self-adjoint operators, J. Math. Soc. Japan 9 (1957), 239-249. MR 0092132 (19:1068c)
  • [5] -, Perturbation of continuous spectra by trace class operators, Proc. Japan Acad. 33 (1957), 260-264. MR 0092133 (19:1068d)
  • [6] -, Wave operators and similarity for some non-selfadjoint operators, Math. Ann. 162 (1966), 258-279. MR 0190801 (32:8211)
  • [7] O. A. Ladyženskaja and L. D. Fadeev, On the perturbation of continuous spectra, Dokl. Akad. Nauk SSSR 120 (1958), 1187-1190. MR 0102750 (21:1536)
  • [8] J. Schwartz, Some non-self-adjoint operators, Comm. Pure Appl. Math. 13 (1960), 609-639. MR 0165372 (29:2656)
  • [9] S. T. Kuroda, Perturbation of continuous spectra by unbounded operators. I, II, J. Math. Soc. Japan 11 (1959), 247-262; 12 (1960), 243-257. MR 0140947 (25:4360)
  • [10] -, An abstract stationary approach to perturbation of continuous spectra and scattering theory, J. Analyse Math. 20 (1967), 57-117. MR 0216331 (35:7165)
  • [11] L. de Branges, Perturbations of self-adjoint transformations, Amer. J. Math. 84 (1962), 543-560. MR 0154132 (27:4083)
  • [12] P. A. Rejto, On gentle perturbations. I, II, Comm. Pure Appl. Math. 16 (1963), 279-303; 17 (1964), 257-292. MR 0154138 (27:4089)
  • [13] M. Š. Birman and M. G. Kreĭn, On the theory of wave operators and scattering operators, Dokl. Akad. Nauk SSSR 144 (1962), 475-478=Soviet Math. Dokl. 3 (1962), 740-744. MR 0139007 (25:2447)
  • [14] M. Š. Birman and S. B. Èntina, A stationary approach in the abstract theory of scattering, Dokl. Akad. Nauk SSSR 155 (1964), 506-508=Soviet Math. Dokl. 5 (1964), 432-434. MR 0164590 (29:1887)
  • [15] K. O. Friedrichs, Perturbation of spectra in Hilbert space, Lectures in Appl. Math., Vol. 3, Amer. Math. Soc. Providence, R. I., 1965. MR 0182883 (32:365)
  • [16] E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Colloq. Publ., Vol. 31, Amer. Math. Soc., Providence, R. I., 1957. MR 0089373 (19:664d)
  • [17] T. Kato, Perturbation theory for linear operators, Springer-Verlag, New York, 1966. MR 0203473 (34:3324)
  • [18] P. R. Halmos, Measure theory, Van Nostrand, Princeton, N. J., 1962. MR 0033869 (11:504d)
  • [19] S. C. Lin, Wave operators and similarity for some operators in Banach spaces, Ph.D. thesis, Univ. of Calif., Berkeley, 1967.
  • [20] N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience, New York, 1958.
  • [21] R. T. Prosser, Convergent perturbation expansions for certain wave operators, J. Math. Phys. 5 (1964), 708-713. MR 0163653 (29:954)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47.48

Retrieve articles in all journals with MSC: 47.48


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1969-0240667-1
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society