Commuting nonselfadjoint operators in Hilbert space : two independent studies

Moshe S. Livšic, Leonid L. Waksman

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.

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  • Commuting nonselfadjoint operators and collective motions of systems.- Harmonic analysis of multi-parameter semigroups of contractions.

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書名 Commuting nonselfadjoint operators in Hilbert space : two independent studies
著作者等 Livšic, Moshe S.
Waksman, Leonid L.
Livsic M. S.
Waksman Leonid L
Livsic Moshe S
シリーズ名 Lecture notes in mathematics
出版元 Springer-Verlag
刊行年月 c1987
ページ数 114 p.
大きさ 25 cm
ISBN 0387183167
NCID BA01030791
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言語 英語
出版国 ドイツ