메뉴 건너뛰기




Volumn 178, Issue 837, 2005, Pages

Lax-Phillips scattering and conservative linear systems: A Cuntz-algebra multidimensional setting

Author keywords

Formal power series; Functional model; Incoming and outgoing space; Noncommuting indeterminants; Row contraction; Row isometry; Scattering function; Unitary colligation

Indexed keywords


EID: 27844440451     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: 10.1090/memo/0837     Document Type: Review
Times cited : (52)

References (54)
  • 1
    • 18844401454 scopus 로고
    • On unitary coupling of semiunitary operators
    • [AA95] [in Russian]
    • [AA95] V.M. Adamjan and D.Z. Arov, On unitary coupling of semiunitary operators, Dokl. Akad. Nauk. Arm. SSR XLIII, 5 (1966), 257-263 [in Russian] =
    • (1966) Dokl. Akad. Nauk. Arm. SSR XLIII , vol.5 , pp. 257-263
    • Adamjan, V.M.1    Arov, D.Z.2
  • 4
    • 0000561456 scopus 로고    scopus 로고
    • Complete Nevanlinna-pick kernels
    • [AM00]
    • [AM00] J. Agler and J.E. McCarthy, Complete Nevanlinna-Pick kernels, J. Functional Analysis 175 (2000), 111-124.
    • (2000) J. Functional Analysis , vol.175 , pp. 111-124
    • Agler, J.1    McCarthy, J.E.2
  • 5
    • 0003194601 scopus 로고    scopus 로고
    • Schur functions, operator colligations, and reproducing kernel pontryagin spaces
    • [ADRS97], Birkhäuser-Verlag, Basel-Boston
    • [ADRS97] D. Alpay, A. Dijksma, J.R. Rovnyak and H. de Snoo, Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces, OT 96, Birkhäuser-Verlag, Basel-Boston, 1997.
    • (1997) OT 96
    • Alpay, D.1    Dijksma, A.2    Rovnyak, J.R.3    De Snoo, H.4
  • 6
    • 0034360839 scopus 로고    scopus 로고
    • Noncommutative interpolation and poisson transforms
    • [AP00]
    • [AP00] A. Arias and G. Popescu, Noncommutative interpolation and Poisson transforms, Israel J. Math. 115 (2000), 205-234.
    • (2000) Israel J. Math. , vol.115 , pp. 205-234
    • Arias, A.1    Popescu, G.2
  • 7
    • 0000326360 scopus 로고    scopus 로고
    • Subalgebras of C* -algebras III: Multivariable operator theory
    • [Arv98]
    • [Arv98] W. Arveson, Subalgebras of C* -algebras III: multivariable operator theory, Acta Math. 181 (1998), 159-228.
    • (1998) Acta Math. , vol.181 , pp. 159-228
    • Arveson, W.1
  • 9
    • 0011552666 scopus 로고    scopus 로고
    • Linear systems, operator model theory and scattering: Multivariable generalizations
    • [Ba00], Operator Theory and Its Applications (Winnipeg, MB, 1998) (Ed. A.G. Ramm, P.N. Shivakumar and A.V. Strauss), Amer. Math. Soc., Providence
    • [Ba00] J.A. Ball, Linear systems, operator model theory and scattering: multivariable generalizations, Operator Theory and Its Applications (Winnipeg, MB, 1998) (Ed. A.G. Ramm, P.N. Shivakumar and A.V. Strauss), Fields Institute Communications Vol. 25, Amer. Math. Soc., Providence, 2000, pp. 151-178
    • (2000) Fields Institute Communications , vol.25 , pp. 151-178
    • Ball, J.A.1
  • 10
    • 0002706744 scopus 로고
    • De Branges-Rovnyak operator models and systems theory: A survey
    • [BaC91] (Ed. H. Bart, I. Gohberg and M.A. Kaashoek), OT 50 Birkhäuser-Verlag, Basel-Boston
    • [BaC91] J.A. Ball and N. Cohen, De Branges-Rovnyak operator models and systems theory: A survey, Topics in Matrix and Operator Theory (Ed. H. Bart, I. Gohberg and M.A. Kaashoek), OT 50 Birkhäuser-Verlag, Basel-Boston, 1991, pp. 93-136.
    • (1991) Topics in Matrix and Operator Theory , pp. 93-136
    • Ball, J.A.1    Cohen, N.2
  • 12
    • 0001858717 scopus 로고    scopus 로고
    • Unitary colligations, reproducing kernel Hilbert spaces, and Nevanlinna-pick interpolation in several variables
    • [BaT98]
    • [BaT98] J.A. Ball and T.T. Trent, Unitary colligations, reproducing kernel Hilbert spaces, and Nevanlinna-Pick interpolation in several variables, J. Functional Analysis 157 (1998), 1-61.
    • (1998) J. Functional Analysis , vol.157 , pp. 1-61
    • Ball, J.A.1    Trent, T.T.2
  • 13
    • 18844366982 scopus 로고    scopus 로고
    • The abstract interpolation problem and commutant lifting: A coordinate-free approach
    • [BaT00] (Ed. H. Bercovici and C. Foiaş), OT115 Birkhäuser-Verlag, Basel-Boston
    • [BaT00] J.A. Ball and T.T. Trent, The abstract interpolation problem and commutant lifting: A coordinate-free approach, Operator Theory and Interpolation: International Workshop on Operator Theory and Applications, IWOTA96 (Ed. H. Bercovici and C. Foiaş), OT115 Birkhäuser-Verlag, Basel-Boston, 2000, pp. 51-83
    • (2000) Operator Theory and Interpolation: International Workshop on Operator Theory and Applications, IWOTA96 , pp. 51-83
    • Ball, J.A.1    Trent, T.T.2
  • 14
    • 0002730245 scopus 로고    scopus 로고
    • Interpolation and commutant lifting for multipliers on reproducing kernel Hilbert spaces with embedding into a ball
    • [BaTV01],Nov. 1997 (Ed. H. Bart, I. Gohberg and A.C.M. Ran), OT 122 Birkhäuser-Verlag, Basel-Boston
    • [BaTV01] J.A. Ball, T.T. Trent and V. Vinnikov, Interpolation and commutant lifting for multipliers on reproducing kernel Hilbert spaces with embedding into a ball, Operator Theory and Analysis: The M.A. Kaashoek Anniversary Volume: Workshop in Amsterdam, Nov. 1997 (Ed. H. Bart, I. Gohberg and A.C.M. Ran), OT 122 Birkhäuser-Verlag, Basel-Boston, 2001, pp. 89-138.
    • (2001) Operator Theory and Analysis: The M.A. Kaashoek Anniversary Volume: Workshop in Amsterdam , pp. 89-138
    • Ball, J.A.1    Trent, T.T.2    Vinnikov, V.3
  • 15
    • 15344345409 scopus 로고    scopus 로고
    • Formal reproducing kernel Hilbert spaces: The commutative and noncommutative settings
    • [BaV03] (Ed. D. Alpay), OT143 Birkhäuser-Verlag, Basel-Boston
    • [BaV03] J.A. Ball and V. Vinnikov, Formal reproducing kernel Hilbert spaces: The commutative and noncommutative settings, Reproducing Kernel Spaces and Applications (Ed. D. Alpay), OT143 Birkhäuser-Verlag, Basel-Boston, 2003, pp. 77-134
    • (2003) Reproducing Kernel Spaces and Applications , pp. 77-134
    • Ball, J.A.1    Vinnikov, V.2
  • 17
    • 0011552666 scopus 로고    scopus 로고
    • Problems on the realization of functions
    • [BaY98], Operator Theory and Its Applications (Winnipeg, MB, 1998) (Ed. A.G. Ramm, P.N. Shivakumar and A.V. Strauss), Amer. Math. Soc., Providence
    • [BaY98] J.A. Ball and N.J. Young, Problems on the realization of functions, Operator Theory and Its Applications (Winnipeg, MB, 1998) (Ed. A.G. Ramm, P.N. Shivakumar and A.V. Strauss), Fields Institute Communications Vol. 25, Amer. Math. Soc., Providence, 2000, pp. 151-178
    • (2000) Fields Institute Communications , vol.25 , pp. 151-178
    • Ball, J.A.1    Young, N.J.2
  • 19
    • 0035249709 scopus 로고    scopus 로고
    • On formal power series representations for uncertain systems
    • [Be01]
    • [Be01] C.L. Beck, On formal power series representations for uncertain systems, IEEE Transactions on Automatic Control 46 (2001), 314-319.
    • (2001) IEEE Transactions on Automatic Control , vol.46 , pp. 314-319
    • Beck, C.L.1
  • 20
    • 0033331760 scopus 로고    scopus 로고
    • A necessary and sufficient minimality condition for uncertain systems
    • [BeD99]
    • [BeD99] C.L. Beck and J. Doyle, A necessary and sufficient minimality condition for uncertain systems, IEEE Transactions on Automatic Control 44 (1999), 1802-1813.
    • (1999) IEEE Transactions on Automatic Control , vol.44 , pp. 1802-1813
    • Beck, C.L.1    Doyle, J.2
  • 21
    • 23644437116 scopus 로고    scopus 로고
    • Measure Schur complements and spectral functions of unitary operators with respect to different scales
    • [BoDK00] (Ed. D. Alpay and V. Vinnikov), OT 123 Birkhäuser, Basel-Boston
    • [BoDK00] S.S. Boiko, V.K. Dubovoy and A.Ya. Kheifets, Measure Schur complements and spectral functions of unitary operators with respect to different scales, Operator Theory, System Theory and Related Topics: The Moshe Livšic Anniversary Volume (Ed. D. Alpay and V. Vinnikov), OT 123 Birkhäuser, Basel-Boston, 2000, pp. 89-138.
    • (2000) Operator Theory, System Theory and Related Topics: The Moshe Livšic Anniversary Volume , pp. 89-138
    • Boiko, S.S.1    Dubovoy, V.K.2    Kheifets, A.Y.3
  • 23
    • 0003228732 scopus 로고
    • Triangular and Jordan representations of linear operators
    • [Bro71], American Mathematical Society, Providence
    • [Bro71] M.S. Brodskiǐ, Triangular and Jordan Representations of Linear Operators, Translations of Mathematical Monographs Volume 32, American Mathematical Society, Providence, 1971.
    • (1971) Translations of Mathematical Monographs , vol.32
    • Brodskiǐ, M.S.1
  • 24
    • 0040795146 scopus 로고
    • Models for n-tuples of noncommuting operators
    • [Bu84]
    • [Bu84] J.W. Bunce, Models for n-tuples of noncommuting operators, J. Functional Analysis 57 (1984), 21-30.
    • (1984) J. Functional Analysis , vol.57 , pp. 21-30
    • Bunce, J.W.1
  • 25
    • 60749118472 scopus 로고    scopus 로고
    • Inverse scattering experiments, structured matrix inequalities, and tensor algebras
    • [CSK02]
    • [CSK02] T. Constantinescu, A.H. Sayed and T. Kailath, Inverse scattering experiments, structured matrix inequalities, and tensor algebras, Linear Alg. Appl. 343/344 (2002), 147-169.
    • (2002) Linear Alg. Appl. , vol.343-344 , pp. 147-169
    • Constantinescu, T.1    Sayed, A.H.2    Kailath, T.3
  • 26
    • 0003305059 scopus 로고    scopus 로고
    • C*-Algebras by example
    • [Da96], American Mathematical Society, Providence
    • [Da96] K.R. Davidson, C*-Algebras by Example, Fields Institute Monograph 6, American Mathematical Society, Providence, 1996.
    • (1996) Fields Institute Monograph , vol.6
    • Davidson, K.R.1
  • 27
    • 0032369135 scopus 로고    scopus 로고
    • The algebraic structure of non-commutative analytic Toeplitz algebras
    • [DaP98a]
    • [DaP98a] K.R. Davidson and D.R. Pitts, The algebraic structure of non-commutative analytic Toeplitz algebras, Math. Ann. 311 (1998), 275-303.
    • (1998) Math. Ann. , vol.311 , pp. 275-303
    • Davidson, K.R.1    Pitts, D.R.2
  • 28
    • 0032128697 scopus 로고    scopus 로고
    • Nevanlinna-pick interpolation for non-commutative analytic Toeplitz algebra
    • [DaP98b]
    • [DaP98b] K.R. Davidson and D.R. Pitts, Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebra, Integral Equations and Operator Theory 31 (1998), 321-337.
    • (1998) Integral Equations and Operator Theory , vol.31 , pp. 321-337
    • Davidson, K.R.1    Pitts, D.R.2
  • 29
    • 0000814346 scopus 로고    scopus 로고
    • Invariant subspaces and hyper-reflexivity for free semigroup algebras
    • [DaP99]
    • [DaP99] K.R. Davidson and D.R. Pitts, Invariant subspaces and hyper-reflexivity for free semigroup algebras, Proc. London Math. Soc. 78 (1999), 401-430.
    • (1999) Proc. London Math. Soc. , vol.78 , pp. 401-430
    • Davidson, K.R.1    Pitts, D.R.2
  • 30
    • 84966242522 scopus 로고
    • A generalization of von Neumann's inequality to the complex ball
    • [Dr78]
    • [Dr78] S.W. Drury, A generalization of von Neumann's inequality to the complex ball, Proc. Amer. Math. Soc. 68 (1978), 300-304.
    • (1978) Proc. Amer. Math. Soc. , vol.68 , pp. 300-304
    • Drury, S.W.1
  • 31
    • 0000692177 scopus 로고
    • Matrices de Hankel
    • [F174]
    • [F174] M. Fliess, Matrices de Hankel, J. Math. pures et appl. 53 (1974), 197-224.
    • (1974) J. Math. Pures et Appl. , vol.53 , pp. 197-224
    • Fliess, M.1
  • 32
    • 0002451378 scopus 로고
    • Models for noncommuting operators
    • [Fr82]
    • [Fr82] A.E. Frazho, Models for noncommuting operators, J. Functional Analysis 48 (1982), 1-11.
    • (1982) J. Functional Analysis , vol.48 , pp. 1-11
    • Frazho, A.E.1
  • 33
    • 0001453002 scopus 로고
    • Complements to models for noncommuting operators
    • [Fr84]
    • [Fr84] A.E. Frazho, Complements to models for noncommuting operators, J. Functional Analysis 59 (1984), 445-461.
    • (1984) J. Functional Analysis , vol.59 , pp. 445-461
    • Frazho, A.E.1
  • 34
    • 0036807490 scopus 로고    scopus 로고
    • The structure of inner multipliers on spaces with complete Nevanlinna Pick kernels
    • [GRS02]
    • [GRS02] D. Greene, S. Richter and C. Sundberg, The structure of inner multipliers on spaces with complete Nevanlinna Pick kernels, J. Functional Analysis 194 (2002), 311-321.
    • (2002) J. Functional Analysis , vol.194 , pp. 311-321
    • Greene, D.1    Richter, S.2    Sundberg, C.3
  • 35
    • 0000076486 scopus 로고
    • The characteristic functions of operator theory and electrical network realization
    • [H72]
    • [H72] J.W. Helton, The characteristic functions of operator theory and electrical network realization, Indiana Univ. Math. J. 22 (1972/73), 403-414.
    • (1972) Indiana Univ. Math. J. , vol.22 , pp. 403-414
    • Helton, J.W.1
  • 36
    • 84910322568 scopus 로고
    • Minimal factorization, linear systems and integral operators
    • [Ka85], Operators and function theory (Lancaster, 1984), Reidel, Dordrecht
    • [Ka85] M.A. Kaashoek, Minimal factorization, linear systems and integral operators, Operators and function theory (Lancaster, 1984), NATO Adv. Sci. Inst. Ser. C Math. Phy. Sci. 153, Reidel, Dordrecht, 1985, pp. 41-86
    • (1985) NATO Adv. Sci. Inst. Ser. C Math. Phy. Sci. , vol.153 , pp. 41-86
    • Kaashoek, M.A.1
  • 37
    • 0141638906 scopus 로고    scopus 로고
    • State space theory of rational matrix functions and application
    • [Ka96], Lectures on Operator Theory and its Applications (Waterloo, ON, 1994), Amer. Math. Soc., Prov., RI
    • [Ka96] M.A. Kaashoek, State space theory of rational matrix functions and application, Lectures on Operator Theory and its Applications (Waterloo, ON, 1994), Fields Inst. Monogr., Amer. Math. Soc., Prov., RI, 1996, pp. 233-333
    • (1996) Fields Inst. Monogr. , pp. 233-333
    • Kaashoek, M.A.1
  • 38
    • 0035655203 scopus 로고    scopus 로고
    • The curvature invariant of a non-commuting N-tuple
    • [Kr01]
    • [Kr01] D.W. Kribs, The curvature invariant of a non-commuting N-tuple, Integral Equations and Operator Theory 41 (2001), 426-454.
    • (2001) Integral Equations and Operator Theory , vol.41 , pp. 426-454
    • Kribs, D.W.1
  • 40
    • 0003480631 scopus 로고
    • Operators, oscillations, waves (open systems)
    • [Li73], American Mathematical Society, Providence
    • [Li73] M.S. Livšic, Operators, Oscillations, Waves (Open Systems), Translations of Mathematical Monographs Volume Thirty-Four, American Mathematical Society, Providence, 1973.
    • (1973) Translations of Mathematical Monographs , vol.34
    • Livšic, M.S.1
  • 41
    • 0000611407 scopus 로고    scopus 로고
    • Invariant subspaces and Nevanlinna-pick kernels
    • [McT00]
    • [McT00] S. McCullough and T.T. Trent, Invariant subspaces and Nevanlinna-Pick kernels, J. Functional Analysis 178 (2000), 226-249.
    • (2000) J. Functional Analysis , vol.178 , pp. 226-249
    • McCullough, S.1    Trent, T.T.2
  • 43
    • 0011287845 scopus 로고
    • A unified approach to function models, and the transcription problem
    • [NiV89] (Ed. H. Dym, S. Goldberg, M.A. Kaashoek and P. Lancaster), OT41 Birkhäuser-Verlag, Basel-Boston
    • [NiV89] N.K. Nikolskii and V.I Vasyunin, A unified approach to function models, and the transcription problem, The Gohberg Anniversary Collection Volume II: Topics in Analysis and Operator Theory (Ed. H. Dym, S. Goldberg, M.A. Kaashoek and P. Lancaster), OT41 Birkhäuser-Verlag, Basel-Boston, 1989, pp. 405-434.
    • (1989) The Gohberg Anniversary Collection VolumeII: Topics in Analysis and Operator Theory , vol.2 , pp. 405-434
    • Nikolskii, N.K.1    Vasyunin, V.I.2
  • 44
    • 0037538983 scopus 로고    scopus 로고
    • Elements of spectral theory in terms of the free function model Part I: Basic constructions
    • [NiV98], Holomorphic Spaces (Ed. S. Axler, J.E. McCarthy and D. Sarason), Cambridge University Press
    • [NiV98] N.K. Nikolskii and V.I. Vasyunin, Elements of spectral theory in terms of the free function model Part I: Basic constructions, Holomorphic Spaces (Ed. S. Axler, J.E. McCarthy and D. Sarason), Mathematical Sciences Research Institute Publications Vol. 33, Cambridge University Press, 1998, pp. 211-302.
    • (1998) Mathematical Sciences Research Institute Publications , vol.33 , pp. 211-302
    • Nikolskii, N.K.1    Vasyunin, V.I.2
  • 45
    • 0000037512 scopus 로고
    • Models for infinite sequences of noncommuting operators
    • [Po89a]
    • [Po89a] G. Popescu, Models for infinite sequences of noncommuting operators, Acta Sci. Math. 53 (1989), 355-368.
    • (1989) Acta Sci. Math. , vol.53 , pp. 355-368
    • Popescu, G.1
  • 46
    • 0002100766 scopus 로고
    • Characteristic functions for infinite sequences of noncommuting operators
    • [Po89b]
    • [Po89b] G. Popescu, Characteristic functions for infinite sequences of noncommuting operators, J. Operator Theory 22 (1989), 51-71.
    • (1989) J. Operator Theory , vol.22 , pp. 51-71
    • Popescu, G.1
  • 47
    • 80955179187 scopus 로고
    • Isometric dilations for infinite sequences of noncommuting operators
    • [Po89c]
    • [Po89c] G. Popescu, Isometric dilations for infinite sequences of noncommuting operators, Trans. Amer. Math. Soc. 316 (1989), 523-536.
    • (1989) Trans. Amer. Math. Soc. , vol.316 , pp. 523-536
    • Popescu, G.1
  • 49
    • 0001925669 scopus 로고
    • Multi-analytic operators on Fock spaces
    • [Po95]
    • [Po95] G. Popescu, Multi-analytic operators on Fock spaces, Math. Ann. 303 (1995), 31-46.
    • (1995) Math. Ann. , vol.303 , pp. 31-46
    • Popescu, G.1
  • 50
    • 0000518649 scopus 로고    scopus 로고
    • Interpolation problems in several variables
    • [Po98]
    • [Po98] G. Popescu, Interpolation problems in several variables, J. Math, Anal. Appl. 227 (1998), 227-250.
    • (1998) J. Math, Anal. Appl. , vol.227 , pp. 227-250
    • Popescu, G.1
  • 51
    • 0033540185 scopus 로고    scopus 로고
    • Poisson transforms on some C*-algebras generated by isometries
    • [Po99]
    • [Po99] G. Popescu, Poisson transforms on some C*-algebras generated by isometries, J. Functional Analysis 161 (1999), 27-61.
    • (1999) J. Functional Analysis , vol.161 , pp. 27-61
    • Popescu, G.1
  • 52
    • 0042198610 scopus 로고    scopus 로고
    • Curvature invariant for Hilbert modules over free semigroup algebras
    • [Po01a]
    • [Po01a] G. Popescu, Curvature invariant for Hilbert modules over free semigroup algebras, Adv. Math. 158 (2001), 264-309.
    • (2001) Adv. Math. , vol.158 , pp. 264-309
    • Popescu, G.1
  • 53
    • 0035255840 scopus 로고    scopus 로고
    • Structure and entropy for positive-definite Toeplitz kernels on free semigroups
    • [Po01b]
    • [Po01b] G. Popescu, Structure and entropy for positive-definite Toeplitz kernels on free semigroups, J. Math. Anal. Appl. 254 (2001), 191-218.
    • (2001) J. Math. Anal. Appl. , vol.254 , pp. 191-218
    • Popescu, G.1
  • 54
    • 84968487163 scopus 로고
    • On unitary dilations of contractions
    • [Sh55]
    • [Sh55] J.J. Schäffer, On unitary dilations of contractions, Proc. Amer. Math. Soc. 6 (1955), 322.
    • (1955) Proc. Amer. Math. Soc. , vol.6 , pp. 322
    • Schäffer, J.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.