Geodesic
On the Relation between the Darlington Realizations of Matrix Functions from the Carathéodory Class and Their $J_{p,r}$-Inner SI-Dilations
Matematičeskie zametki, Tome 90 (2011) no. 6, pp. 821-832 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper is devoted to establishing a two-sided relation between the Darlington realizations of matrix functions from the Carathéodory class $\mathscr C^{p\times p}\Pi$ and their $J_{p,r}$-inner SI-dilations.
Keywords: Darlington realization of matrix functions, Carathéodory class of functions, SI (scattering-impedance)-dilation, meromorphic function, Smirnov class of functions. 
@article{MZM_2011_90_6_a1,
     author = {D. Z. Arov and N. A. Rozhenko},
     title = {On the {Relation} between the {Darlington} {Realizations} of {Matrix} {Functions} from the {Carath\'eodory} {Class} and {Their} $J_{p,r}${-Inner} {SI-Dilations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {821--832},
     year = {2011},
     volume = {90},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_6_a1/}
}
TY  - JOUR
AU  - D. Z. Arov
AU  - N. A. Rozhenko
TI  - On the Relation between the Darlington Realizations of Matrix Functions from the Carathéodory Class and Their $J_{p,r}$-Inner SI-Dilations
JO  - Matematičeskie zametki
PY  - 2011
SP  - 821
EP  - 832
VL  - 90
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_2011_90_6_a1/
LA  - ru
ID  - MZM_2011_90_6_a1
ER  - 
%0 Journal Article
%A D. Z. Arov
%A N. A. Rozhenko
%T On the Relation between the Darlington Realizations of Matrix Functions from the Carathéodory Class and Their $J_{p,r}$-Inner SI-Dilations
%J Matematičeskie zametki
%D 2011
%P 821-832
%V 90
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_2011_90_6_a1/
%G ru
%F MZM_2011_90_6_a1
D. Z. Arov; N. A. Rozhenko. On the Relation between the Darlington Realizations of Matrix Functions from the Carathéodory Class and Their $J_{p,r}$-Inner SI-Dilations. Matematičeskie zametki, Tome 90 (2011) no. 6, pp. 821-832. http://geodesic.mathdoc.fr/item/MZM_2011_90_6_a1/

[1] D. Z. Arov, “O metode Darlingtona v issledovanii dissipativnykh sistem”, Dokl. AN SSSR, 201:3 (1971), 559–562 | MR | Zbl

[2] D. Z. Arov, “Realizatsiya matrits-funktsii po Darlingtonu”, Izv. AN SSSR. Ser. matem., 37:6 (1973), 1299–1331 | MR | Zbl

[3] D. Z. Arov, “Realizatsiya kanonicheskoi sistemy s dissipativnym granichnym usloviem na odnom kontse segmenta po koeffitsientu dinamicheskoi podatlivosti”, Sib. matem. zhurn., 16:3 (1975), 440–463 | MR | Zbl

[4] S. Darlington, “Synthesis of reactance $4$-poles which produce prescribed insertion loss characteristics including special applications to filter design”, J. Math. Phys. Mass. Inst. Tech., 18 (1939), 257–353 | MR

[5] D. Z. Arov, N. A. Rozhenko, “$J_{p,m}$-vnutrennie dilatatsii matrits-funktsii klassa Karateodori, imeyuschikh psevdoprodolzhenie”, Algebra i analiz, 19:3 (2007), 76–105 | MR

[6] D. Z. Arov, N. A. Rozhenko, “Passivnye sistemy soprotivleniya s poteryami kanalov rasseyaniya”, Ukr. matem. zhurn., 59:5 (2007), 618–649 | MR | Zbl

[7] D. Z. Arov, N. A. Rozhenko, “K teorii passivnykh sistem soprotivleniya s poteryami kanalov rasseyaniya”, Issledovaniya po lineinym operatoram i teorii funktsii. 36, Zap. nauchn. sem. POMI, 355, POMI, SPb., 2008, 37–71 | Zbl

[8] P. Dewilde, “Input-output description of roomy systems”, SIAM J. Control Optimization, 14:4 (1976), 712–736 | MR | Zbl

[9] R. G. Douglas, J. W. Helton, “Inner dilations of analytic matrix functions and Darlington synthesis”, Acta Sci. Math. (Szeged), 34 (1973), 61–67 | MR | Zbl

[10] D. Z. Arov, H. Dym, $J$-Contractive Matrix Valued Functions and Related Topics, Encyclopedia Math. Appl., 116, Cambrige Univ. Press, Cambridge, 2008 | MR | Zbl

[11] V. E. Katsnelson, B. Kirstein, “On the theory of matrix-valued functions belonging to the Smirnov class”, Topics in Interpolation Theory, Oper. Theory Adv. Appl., 95, Birkhäuser, Basel, 1997, 299–350 | MR | Zbl