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Spectral theory for contraction semigroups on Hilbert space. (English) Zbl 0326.47038

MSC:
47D03 Groups and semigroups of linear operators
47A10 Spectrum, resolvent
47A20 Dilations, extensions, compressions of linear operators
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[1] R. G. Douglas, P. S. Muhly, and Carl Pearcy, Lifting commuting operators, Michigan Math. J. 15 (1968), 385 – 395. · Zbl 0174.18202
[2] Paul A. Fuhrmann, On the corona theorem and its application to spectral problems in Hilbert space, Trans. Amer. Math. Soc. 132 (1968), 55 – 66. · Zbl 0187.38002
[3] Paul A. Fuhrmann, A functional calculus in Hilbert spaces based on operator valued analytic functions, Israel J. Math. 6 (1968), 267 – 278. · Zbl 0187.38003 · doi:10.1007/BF02760259 · doi.org
[4] L. Gearhart, On the spectral theory of the translation semigroup and its commutant, Thesis, Univ. of Illinois, Chicago, 1975.
[5] Paul R. Halmos, Shifts on Hilbert spaces, J. Reine Angew. Math. 208 (1961), 102 – 112. · Zbl 0107.09802 · doi:10.1515/crll.1961.208.102 · doi.org
[6] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. · Zbl 0078.10004
[7] Peter D. Lax, Translation invariant spaces, Acta Math. 101 (1959), 163 – 178. · Zbl 0085.09102 · doi:10.1007/BF02559553 · doi.org
[8] Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. · Zbl 0186.16301
[9] James W. Moeller, On the spectra of some translation invariant spaces, J. Math. Anal. Appl. 4 (1962), 276 – 296. · Zbl 0116.32301 · doi:10.1016/0022-247X(62)90055-0 · doi.org
[10] J. W. Moeller, Translation invariant spaces with zero-free spectra, Duke Math. J. 31 (1964), 99 – 108. · Zbl 0187.37902
[11] R. S. Phillips, Spectral theory for semi-groups of linear operators, Trans. Amer. Math. Soc. 71 (1951), 393 – 415. · Zbl 0045.21502
[12] Béla Sz.-Nagy and Ciprian Foiaş, Harmonic analysis of operators on Hilbert space, Translated from the French and revised, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970. · Zbl 0201.45003
[13] Béla Sz.-Nagy and Ciprian Foiaş, On the structure of intertwining operators, Acta Sci. Math. (Szeged) 35 (1973), 225 – 254. · Zbl 0272.47010
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