Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators
Data(s) |
18/06/2012
18/06/2012
2005
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Resumo |
2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12. In this paper classes of K^r -operators are considered – the classes of bounded and unbounded operators A with equal domains of A and A*, finite dimensional imaginary parts and presented as a coupling of a dissipative operator and an antidissipative one with real absolutely continuous spectra and the class of unbounded dissipative K^r -operators A with different domains of A and A* and with real absolutely continuous spectra. Their triangular models are presented. The asymptotics of the corresponding continuous curves with generators from these classes are obtained in an explicit form. With the help of the obtained asymptotics the scattering theory for the couples (A*, A) when A belongs to the introduced classes is constructed. Partially supported by Grant MM-1403/04 of MESC and by Scientific Research Grants 19/13.03.2003 and 26/01.04.2004 of Shumen University. |
Identificador |
Serdica Mathematical Journal, Vol. 31, No 1-2, (2005), 95p-174p 1310-6600 |
Idioma(s) |
en |
Publicador |
Institute of Mathematics and Informatics Bulgarian Academy of Sciences |
Palavras-Chave | #Unbounded Operator #Operator Colligation #Characteristic Function #Nondissipative Curve #Correlation Function #Wave Operator #Scattering Operator |
Tipo |
Article |