LEADER 03427nam 22006255 450 001 996466474703316 005 20220204012054.0 010 $a3-540-47877-9 024 7 $a10.1007/BFb0078925 035 $a(CKB)1000000000437533 035 $a(SSID)ssj0000321942 035 $a(PQKBManifestationID)12064706 035 $a(PQKBTitleCode)TC0000321942 035 $a(PQKBWorkID)10281221 035 $a(PQKB)11480993 035 $a(DE-He213)978-3-540-47877-5 035 $a(MiAaPQ)EBC5610970 035 $a(Au-PeEL)EBL5610970 035 $a(OCoLC)1079007266 035 $a(MiAaPQ)EBC6842599 035 $a(Au-PeEL)EBL6842599 035 $a(OCoLC)793079025 035 $a(PPN)155238000 035 $a(EXLCZ)991000000000437533 100 $a20121227d1987 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aCommuting Nonselfadjoint Operators in Hilbert Space$b[electronic resource] $eTwo Independent Studies /$fby Moshe S. Livsic, Leonid L. Waksman 205 $a1st ed. 1987. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1987. 215 $a1 online resource (VI, 118 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1272 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-18316-7 330 $aClassification of commuting non-selfadjoint operators is one of the most challenging problems in operator theory even in the finite-dimensional case. The spectral analysis of dissipative operators has led to a series of deep results in the framework of unitary dilations and characteristic operator functions. It has turned out that the theory has to be based on analytic functions on algebraic manifolds and not on functions of several independent variables as was previously believed. This follows from the generalized Cayley-Hamilton Theorem, due to M.S.Livsic: "Two commuting operators with finite dimensional imaginary parts are connected in the generic case, by a certain algebraic equation whose degree does not exceed the dimension of the sum of the ranges of imaginary parts." Such investigations have been carried out in two directions. One of them, presented by L.L.Waksman, is related to semigroups of projections of multiplication operators on Riemann surfaces. Another direction, which is presented here by M.S.Livsic is based on operator colligations and collective motions of systems. Every given wave equation can be obtained as an external manifestation of collective motions. The algebraic equation mentioned above is the corresponding dispersion law of the input-output waves. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1272 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aAnalysis. 676 $a515 700 $aLivsic$b Moshe S$4aut$4http://id.loc.gov/vocabulary/relators/aut$056199 702 $aWaksman$b Leonid L$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466474703316 996 $aCommuting nonselfadjoint operators in Hilbert space$9262371 997 $aUNISA