Multivariable backward-shift-invariant subspaces and observability operators
Tóm tắt
Từ khóa
Tài liệu tham khảo
Agler J., McCarthy J.E. (2002). Pick interpolation and Hilbert function spaces, Graduate Studies in Mathematics, Volume 44, Providence: American Mathematical Society.
Alpay D., Dijksma A., Rovnyak J. (2003). A theorem of Beurling-Lax type for Hilbert spaces of functions analytic in the unit ball. Integral Equations and Operator Theory 47(3): 251–274
Alpay D., Dubi C. (2005). On commuting operators solving Gleason’s problem. Proceedings of the American Mathematical Society 133(11): 3285–3293
Ambrozie C.-G., Engliš M., Müller V. (2002). Operator tuples and analytic models over general domains in $${\mathbb{C}^{n}}$$ . Jounrnal of the Operator Theory 47, 287–302
Arazy J., Engliš M. (2003). Analytic models for commuting operator tuples on bounded symmetric domains. Transactions of the American Mathematical Society 355(2): 837–864
Arias A., Popescu G. (2000). Non-commutative interpolation and Poisson transforms. Israel Journal of Mathematics 115, 205–234
Arveson W. (1998). Subalgebras of C * algebras III: Multivariable operator theory. Acta Mathematica 181, 159–228
Arveson W. (2000). The curvature invariant of a Hilbert module over $${{\mathbb{C}[z_{1}, \dots, z_{d}]}}$$ . Journal für die Reine und Angewandte Mathematik 522, 173–236
Ball J.A., Bolotnikov V., & Fang Q. (2007a). Transfer-function realization for multipliers of the Arveson space. Journal of Mathematical Analysis and Applications, (to appear).
Ball J.A., Bolotnikov V., & Fang Q. (2007b). Schur-class multipliers on the Fock space: de Branges-Rovnyak reproducing kernel spaces and transfer-function realizations, in Teberiu Constantinescu Memorial Volume, Bucharest: Theta (to appear).
Ball J.A., Groenewald G., Malakorn T. (2005). Structured noncommutative multidimensional linear system. SIAM Journal on Control and Optimization 44(4): 1474–1528
Ball J.A., Groenewald G., & Malakorn T. (2006). Conservative structured noncommutative multidimensional linear systems. In D. Alpay & I. Gohberg (Eds.), The state space method: Generalizations and applications. (pp. 179–223), OT 161. Basel: Birkhäuser.
Ball J.A., Kriete T.L. (1987). Operator-valued Nevanlinna-Pick kernels and the functional models for contraction operators. Integral Equations and Operator Theory 10(1): 17–61
Ball J.A., Sadosky C., Vinnikov V. (2005). Conservative input-state-output systems with evolution on a multidimensional integer lattice. Multidimensional System Signal Processes 16(2): 133–198
Ball J.A., & Vinnikov V. (2003). Formal reproducing kernel Hilbert spaces: The commutative and noncommutative settings. In D. Alpay (Ed.), Reproducing Kernel spaces and applications, (pp. 77–134), OT 143. Basel: Birkhäuser.
Ball J.A., & Vinnikov V. (2005). Lax-Phillips scattering and conservative linear systems: A Cuntz-algebra multidimensional setting. Memoirs of the American Mathematical Society, 178(837).
Bhattacharyya T., Eschmeier J., Sarkar J. (2005). Characteristic function of a pure commuting contractive tuple. Integral Equations and Operator Theory 53(1): 23–32
Bhattacharyya T., Sarkar J. (2006). Characteristic function for polynomially contractive commuting tuples. Journal of Mathematical Analysis and Applications 321(1): 242–259
Bolotnikov V., Rodman L. (2002). Finite dimensional backward shift invariant subspaces of Arveson spaces. Linear Algebra Applications 349, 265–282
Bolotnikov V., Rodman L. (2004). Finite dimensional backward shift invariant subspaces of a class of reproducing kernel Hilbert spaces. Linear Multilinear Algebra 52, 321–334
de Branges L., Rovnyak J. (1966). Canonical models in quantum scattering theory. In: Wilcox C.H., (eds) Perturbation theory and its applications in Quantum Mechanics. New York, Wiley, pp. 295–392
Chalendar I. (2003). The operator-valued Poisson kernel and its applications. Irish Mathematical Society Bulletin 51, 21–44
Curto R.E., Vasilescu F.H. (1993). Standard operator models in the polydisc. Indiana University Mathematics Journal 42(3): 791–810
Curto R.E., Vasilescu F.H. (1995). Standard operator models in the polydisc, II. Indiana Univiversity Mathematics Journal 44(3): 727–746
Davidson K., Pitts D. (1998). Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebras. Integral Equations and Operator Theory 31(3): 321–337
Davidson K.R.(2001). Free semigroup algebras: a survey. In A. A. Borichev, & N. K. Nikolski, (Eds.) Systems, approximation, singular integral operators, and related topics (pp. 209–240), OT 129, Basel: Birkhäuser.
Douglas R.G. (1974). Canonical models, In Topics in operator theory. Mathemetical Surveys 13, 161–218
Drury S.W. (1978). A generalization of von Neumann’s inequality to the complex ball. Proceedings of the American Mathematical Society 68(3): 300–304
Dym H. (1989). J contractive matrix functions, reproducing kernel Hilbert spaces and interpolation, CBMS 71 Providence: American Mathematical Society.
Galkowski K. (2005). Minimal state-space realization for a class of nD systems. In: Kaashoek M.A., Seatzu S., van der Mee C. (eds), Recent advances in operator theory and its applications (pp. 179–194), OT 160, Basel: Birkhäuser.
Gleason A.M. (1964). Finitely generated ideals in Banach algebras. Journal of Mathematics and Mechanics 13, 125–132
Greene D., Richter S., Sundberg C. (2002). The structure of inner multipliers on spaces with complete Nevanlinna-Pick kernels. Journal of Functional Analysis 194, 311–321
Heinz E. (1952). Ein v. Neumannsher Satz über beschränkte Operatoren im Hilbertschen Raum, Nachrichten der Akademie der Wissenschaften in Göttingen. II Mathematisch-Physikalische Klasse, 5–6.
Helton J.W. (1972/1973). The characteristic functions of operator theory and electrical network realization. Indiana University Mathematics Journal, 22, 403–414
Helton J.W. (1974). Discrete time systems, operator models and scattering theory. Journal of Functional Analysis 16, 15–38
Henkin G.M. (1971). The approximation of functions in pseudo-convex domains and a theorem of Z.L. Leĭbenzon. Bulletin de l’Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques, 19, 37–42
McCullough S., Trent T.T. (2000). Invariance subspaces and Nevanlinna-Pick kernels. Journal of Functional Analysis 178(1): 226–249
Müller V., Vasilescu F.-H. (1993). Standard models for some commuting multioperators. Procedings of the American Mathematical Society 117(4): 979–989
Sz.-Nagy B., Foiaş C. (1970). Harmonic analysis of operators on Hilbert space. Amsterdam-London, North-Holland
Popescu G. (1989a). Models for infinite sequences of noncommuting operators. Acta Scientiarum Mathematicarum (Szeged) 53, 355–368
Popescu G. (1989b). Isometric dilations for infinite sequences of noncommuting operators. Transactions of the American Mathematical Society 316: 523–536
Popescu G. (1989c). Characteristic functions for infinite sequences of noncommuting operators. Journal of Operator Theory 22(1): 51–71
Popescu G. (1989d). Multi-analytic operators and some factorization theorems. Indiana University Mathematics Journal 38(3): 693–710
Popescu G. (1991). von Neumann inequality for $${(B(\mathcal{H})^{n})_{1}}$$ . Mathematica Scandinavica, 68, 292-304
Popescu G. (1998). Interpolation problems in several variables. Journal of Mathematical Analysis and Applications 227(1): 227–250
Popescu G. (1999). Poisson transforms on some C*-algebras generated by isometries. Journal of Functional Analysis 161(1): 27–61
Popescu G. (2006). Operator theory on noncommutative varieties. Indiana University Mathematics Journal 55(2): 389–442
Popescu G. Operator theory on noncommutative varieties II. Proceedings of the American Mathematical Society (to appear).
Pott S. (1999). Standard models under polynomial positivity conditions. Journal of Operator Theory 41, 365–389