Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2675

 Title: Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators Authors: Zolotarev, Vladimir A.Hatamleh, Raéd Keywords: ColligationsNon-Dissipative OperatorFunctional ModelResolvent Operator Issue Date: 2009 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 35, No 4, (2009), 343p-358p Abstract: A relation between an arbitrary bounded operator A and dissipative operator A+, built by A in the following way A+ = A+ij*Q-j, where A-A* = ij*Jj, (J = Q+-Q- is involution), is studied. The characteristic functions of the operators A and A+ are expressed by each other using the known Potapov-Ginsburg linear-fractional transformations. The explicit form of the resolvent (A-lI)-1 is expressed by (A+-lI)-1 and (A+*-lI)-1 in terms of these transformations. Furthermore, the functional model [10, 12] of non-dissipative operator A in terms of a model for A+, which evolves the results, was obtained by Naboko, S. N. [7]. The main constructive elements of the present construction are shown to be the elements of the Potapov-Ginsburg transformation for corresponding characteristic functions. A relation between an arbitrary bounded operator A and dissipative operator A+, built by A in the following way A+ = A + iϕ Description: 2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48. URI: http://hdl.handle.net/10525/2675 ISSN: 1310-6600 Appears in Collections: Volume 35, Number 4

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