# Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators

Zolotarev, Vladimir A.; Hatamleh, Raéd

Serdica Mathematical Journal (2009)

- Volume: 35, Issue: 4, page 343-358
- ISSN: 1310-6600

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topZolotarev, Vladimir A., and Hatamleh, Raéd. "Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators." Serdica Mathematical Journal 35.4 (2009): 343-358. <http://eudml.org/doc/281390>.

@article{Zolotarev2009,

abstract = {2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.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},

author = {Zolotarev, Vladimir A., Hatamleh, Raéd},

journal = {Serdica Mathematical Journal},

keywords = {Colligations; Non-Dissipative Operator; Functional Model; Resolvent Operator; colligations; non-dissipative operator; functional model; resolvent operator},

language = {eng},

number = {4},

pages = {343-358},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators},

url = {http://eudml.org/doc/281390},

volume = {35},

year = {2009},

}

TY - JOUR

AU - Zolotarev, Vladimir A.

AU - Hatamleh, Raéd

TI - Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators

JO - Serdica Mathematical Journal

PY - 2009

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 35

IS - 4

SP - 343

EP - 358

AB - 2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.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

LA - eng

KW - Colligations; Non-Dissipative Operator; Functional Model; Resolvent Operator; colligations; non-dissipative operator; functional model; resolvent operator

UR - http://eudml.org/doc/281390

ER -

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