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Wave operators and similarity for some non-selfadjoint operators

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Bibliography

  1. Dunford, N.: A survey of the theory of spectral operators. Bull. Am. Math. Soc.64, 217–274 (1958).

    Google Scholar 

  2. Fadeev, L. D.: On the Friedrichs model in the perturbation theory of continuous spectrum. Trudy Mat. Inst. im. V. A. Steklova73, 292–313 (1964) (Russian).

    Google Scholar 

  3. Friedrichs, K. O.: Über die Spektralzerlegung eines Integraloperators. Math. Ann.115, 249–272 (1938).

    Google Scholar 

  4. —— On the perturbation of continuous spectra. Comm. Appl. Math.1, 361–406 (1948).

    Google Scholar 

  5. Helson, H.: Lectures on invariant subspaces. New York-London: Academic Press 1964.

    Google Scholar 

  6. Hille, E., andR. S. Phillips: Functional analysis and semi-groups. Revised Ed. Am. Math. Soc. Colloq. Publ. Vol.31 (1957).

  7. Hoffman, K.: Banach spaces of analytic functions. Englewood Cliffs: Prentice-Hall 1962.

    Google Scholar 

  8. Ikebe, T.: Eigenfunktion expansions associated with the Schroedinger operators and their applications to scattering theory. Arch. Rational Mech. Anal.5, 1–34 (1960).

    Google Scholar 

  9. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer-Verlag 1966.

    Google Scholar 

  10. Köthe, G.: Topologische lineare Räume, I. Berlin-Göttingen-Heidelberg: Springer-Verlag 1960.

    Google Scholar 

  11. Kuroda, S. T.: On the existence and the unitary property of the scattering operator. Nuovo Cimento12, 431–454 (1959).

    Google Scholar 

  12. Moser, J.: Störungstheorie des kontinuierlichen Spektrums für gewöhnliche Differentialgleichungen zweiter Ordnung. Math. Ann.125, 366–393 (1953).

    Google Scholar 

  13. Prosser, R. T.: Convergent perturbation expansions for certain wave operators. J. Mathematical Phys.5, 708–713 (1964).

    Google Scholar 

  14. Rejto, P. A.: On gentle perturbations, I and II. Comm. Pure Appl. Math.16, 279–303 (1963);17, 257–292 (1964).

    Google Scholar 

  15. Scadron, M., S. Weinberg, andJ. Wright: Functional analysis and scattering theory. Phys. Rev.135, B202–207 (1964).

    Google Scholar 

  16. Schwartz, J.: Some non-selfadjoint operators. Comm. Pure Appl. Math.13, 609–639 (1960).

    Google Scholar 

  17. Stone, M. H.: Linear transformations in Hilbert space and their applications to analysis. Am. Math. Soc. Colloq. Publ. Vol.15 (1932).

  18. Titchmarsh, E. C.: Introduction to the theory of Fourier integrals. Oxford University Press 1948.

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  1. Berkeley

    Tosio Kato

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  1. Tosio Kato
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Dedicated to ProfessorGottfried Köthe on his 60th birthday

This work was partly supported by Air Force Office of Scientific Research Grant 553–64.

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Kato, T. Wave operators and similarity for some non-selfadjoint operators. Math. Ann. 162, 258–279 (1966). https://doi.org/10.1007/BF01360915

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