The aim of this paper is to give a very brief account of some applications of the method of unitary extensions of isometries to interpolation and extension problems.
Centro de Matemáticas, Facultad de Ciencias, José M. Montero 3006, ap. 503, Montevideo, Uruguay
Bibliografia
[AF] R. Arocena and F. Montans, On a general bidimensional extrapolation problem, Colloq. Math. 64 (1993), 3-12.
[A.1] R. Arocena, Schur analysis of a class of translation invariant forms, in: Analysis and Partial Differential Equations: A Collection of Papers dedicated to Mischa Cotlar, C. Sadosky (ed.), Marcel Dekker, New York and Basel, 1990.
[A.2] R. Arocena, Some remarks on lifting and interpolation problems, Rev. Un. Mat. Argentina 37 (1991), 200-211.
[A.3] R. Arocena, Unitary colligations and parametrization formulas, Ukrainian Math. J. 46 (1994), 147-154.
[A.4] R. Arocena, On the Nagy-Foiaş-Parrott commutant lifting theorem, in: Contemp. Math. 189, Amer. Math. Soc., 1995, 55-64.
[A.5] R. Arocena, Unitary extensions of isometries and interpolation problems: (1) dilation and lifting theorems, Publ. Mat. Uruguay 6 (1995), 137-158.
[AG] D. Z. Arov and L. Z. Grossman, Scattering matrices in the theory of unitary extensions of isometric operators, Soviet Math. Dokl. 27 (1983), 518-522.
[DG.1] H. Dym and I. Gohberg, Extensions of kernels of Fredholm operators, J. Analyse Math. 42 (1982/83), 51-97.
[DG.2] H. Dym and I. Gohberg, A new class of contractive interpolants and maximun entropy principles, in: Oper. Theory Adv. Appl. 29, Birkhäuser, 1988, 117-150.
[FF] C. Foiaş and A. E. Frazho, The Commutant Lifting Approach to Interpolation Problems, Birkhäuser, Basel, 1990.
[FFG] C. Foiaş, A. E. Frazho and I. Gohberg, Central intertwining lifting, maximum entropy and their permanence, Integral Equations Operator Theory 18 (1994), 166-201.
[GKW.1] I. Gohberg, M. A. Kaashoek and H. J. Woerdeman, The band method for positive and contractive extension problems, J. Operator Theory 22 (1989), 109-115.
[GKW.2] I. Gohberg, M. A. Kaashoek and H. J. Woerdeman, The band method for positive and contractive extension problems. An alternative version and new applications, Integral Equations Operator Theory 12 (1989), 343-382.
[GKW.3] I. Gohberg, M. A. Kaashoek and H. J. Woerdeman, A maximum entropy principle in the general framework of the band method, J. Funct. Anal. 95 (1991), 231-254.
[N] N. K. Nikol'skiĭ, Treatise on the Shift Operator, Springer, New York, 1986.
[P] S. Parrott, On a quotient norm and the Sz.-Nagy-Foiaş lifting theorem, J. Funct. Anal. 30 (1978), 311-328.
[S] D. Sarason, Generalized interpolation in $H^∞$, Trans. Amer. Math. Soc. 127 (1967), 179-203.
[Sz.-NF] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970.
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Bibliografia
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