Commuting Nonselfadjoint Operators in Hilbert Space: Two Independent Studies: 1272 (Lecture Notes in Mathematics) - Softcover

Livsic, Moshe S.

 
9783540183167: Commuting Nonselfadjoint Operators in Hilbert Space: Two Independent Studies: 1272 (Lecture Notes in Mathematics)
Softcover
ISBN 10: 3540183167 ISBN 13: 9783540183167
Verlag: Springer Berlin Heidelberg, 2008

Inhaltsangabe

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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Reseña del editor

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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Verlag
Springer Berlin Heidelberg
Erscheinungsdatum
2008
Sprache
Englisch
ISBN 10 
3540183167
ISBN 13 
9783540183167
Einband
Tapa blanda
Anzahl der Seiten
120
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9780387183169: Commuting Nonselfadjoint Operators in Hilbert Space (Lecture Notes in Mathematics, Vol 1272)

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ISBN 10:  0387183167 ISBN 13:  9780387183169
Softcover