Wave operators and similarity for some non-selfadjoint operators. (English) Zbl 0139.31203

Full Text: DOI EuDML


[1] Dunford, N.: A survey of the theory of spectral operators. Bull. Am. Math. Soc.64, 217-274 (1958). · Zbl 0088.32102
[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).
[3] Friedrichs, K. O.: ?ber die Spektralzerlegung eines Integraloperators. Math. Ann.115, 249-272 (1938). · Zbl 0018.07001
[4] ?? On the perturbation of continuous spectra. Comm. Appl. Math.1, 361-406 (1948). · Zbl 0031.31204
[5] Helson, H.: Lectures on invariant subspaces. New York-London: Academic Press 1964. · Zbl 0119.11303
[6] Hille, E., andR. S. Phillips: Functional analysis and semi-groups. Revised Ed. Am. Math. Soc. Colloq. Publ. Vol.31 (1957). · Zbl 0078.10004
[7] Hoffman, K.: Banach spaces of analytic functions. Englewood Cliffs: Prentice-Hall 1962. · Zbl 0117.34001
[8] Ikebe, T.: Eigenfunktion expansions associated with the Schroedinger operators and their applications to scattering theory. Arch. Rational Mech. Anal.5, 1-34 (1960). · Zbl 0145.36902
[9] Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer-Verlag 1966. · Zbl 0148.12601
[10] K?the, G.: Topologische lineare R?ume, I. Berlin-G?ttingen-Heidelberg: Springer-Verlag 1960.
[11] Kuroda, S. T.: On the existence and the unitary property of the scattering operator. Nuovo Cimento12, 431-454 (1959). · Zbl 0084.44801
[12] Moser, J.: St?rungstheorie des kontinuierlichen Spektrums f?r gew?hnliche Differentialgleichungen zweiter Ordnung. Math. Ann.125, 366-393 (1953). · Zbl 0050.31304
[13] Prosser, R. T.: Convergent perturbation expansions for certain wave operators. J. Mathematical Phys.5, 708-713 (1964).
[14] Rejto, P. A.: On gentle perturbations, I and II. Comm. Pure Appl. Math.16, 279-303 (1963);17, 257-292 (1964). · Zbl 0133.08002
[15] Scadron, M., S. Weinberg, andJ. Wright: Functional analysis and scattering theory. Phys. Rev.135, B202-207 (1964). · Zbl 0127.18902
[16] Schwartz, J.: Some non-selfadjoint operators. Comm. Pure Appl. Math.13, 609-639 (1960). · Zbl 0096.08901
[17] Stone, M. H.: Linear transformations in Hilbert space and their applications to analysis. Am. Math. Soc. Colloq. Publ. Vol.15 (1932). · Zbl 0005.40003
[18] Titchmarsh, E. C.: Introduction to the theory of Fourier integrals. Oxford University Press 1948. · Zbl 0031.03202
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.