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A Decomposition Theorem for the Translation-Invariant Subspace of a Canonical Differential Operator

  • M. V. Buslaeva
Chapter
Part of the Seminars in Mathematics book series (SM)

Abstract

Let H be a unitary space of even dimension 2 m, and let y be a linear operator in H for which y* = − y, y2 = − I. The orthogonal projectors P± = 1/2. (I ± i y) define two subspaces H+ and H in H. We shall assume that H+. = dim H = m. We denote by H0 a certain subspace in H of dimension m, whose elements satisfy the relation (y f, g) = 0, f, g ∈ H0.

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Literature Cited

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    Adamyan, V. M., Dokl. Akad. Nauk SSSR, Vol, 178, No. 1 (1969).Google Scholar
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    Lax, P. D., and Phillips, R. S., Scattering Theory, Academic Press (1967).Google Scholar
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    Nikol’skii, N. K., and Pavlov, B. S., Dokl. Akad. Nauk SSSR, Vol. 184, No. 3 (1969).Google Scholar
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    Zak, M. V., Vestnik Leningrad. Univ. (LGU), 19 (4) (1969).Google Scholar

Copyright information

© Springer Science+Business Media New York 1972

Authors and Affiliations

  • M. V. Buslaeva

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