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

Zolotarev, 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 -