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＜電子ブック＞
Commuting Nonselfadjoint Operators in Hilbert Space : Two Independent Studies / by Moshe S. Livsic, Leonid L. Waksman
(Lecture Notes in Mathematics. ISSN:16179692 ; 1272)

版	1st ed. 1987.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	1987
本文言語	英語
大きさ	VI, 118 p : online resource
冊子体	Commuting nonselfadjoint operators in Hilbert space : two independent studies / Moshe S. Livšic, Leonid L. Waksman ; : gw,: us
著者標目	*Livsic, Moshe S author Waksman, Leonid L author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis FREE:Analysis
一般注記	Classification of commuting non-selfadjoint operators is one of the most challenging problems in operator theory even in the finite-dimensional case. The spectral analysis of dissipative operators has led to a series of deep results in the framework of unitary dilations and characteristic operator functions. It has turned out that the theory has to be based on analytic functions on algebraic manifolds and not on functions of several independent variables as was previously believed. This follows from the generalized Cayley-Hamilton Theorem, due to M.S.Livsic: "Two commuting operators with finite dimensional imaginary parts are connected in the generic case, by a certain algebraic equation whose degree does not exceed the dimension of the sum of the ranges of imaginary parts." Such investigations have been carried out in two directions. One of them, presented by L.L.Waksman, is related to semigroups of projections of multiplication operators on Riemann surfaces. Another direction, which is presented here by M.S.Livsic is based on operator colligations and collective motions of systems. Every given wave equation can be obtained as an external manifestation of collective motions. The algebraic equation mentioned above is the corresponding dispersion law of the input-output waves Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/BFb0078925

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