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020 _a9783540478775
_9978-3-540-47877-5
024 7 _a10.1007/BFb0078925
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
100 1 _aLivšic, Moshe S.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aCommuting Nonselfadjoint Operators in Hilbert Space
_h[electronic resource] :
_bTwo Independent Studies /
_cby Moshe S. Livšic, Leonid L. Waksman.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1987.
300 _aVI, 118 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1272
520 _aClassification 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.
650 0 _aGlobal analysis (Mathematics).
650 1 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
700 1 _aWaksman, Leonid L.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662163139
776 0 8 _iPrinted edition:
_z9783540183167
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1272
856 4 0 _uhttps://doi.org/10.1007/BFb0078925
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10582
_d10582