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References
Daniel Alpay, Aad Dijksma, and James Rovnyak, On Nudel\('\)man’s problem and indefinite interpolation in the generalized Schur and Nevanlinna classes, Complex Anal. Oper. Theory 14 (2020), no. 1, Art. 25, 30. MR 4060499
Daniel Alpay, Aad Dijksma, James Rovnyak, and Hendrik de Snoo, Schur functions, operator colligations, and reproducing kernel Pontryagin spaces, Operator Theory: Advances and Applications, vol. 96, Birkhäuser Verlag, Basel, 1997. MR 1465432
Rodrigo Arocena, Tomas Ya. Azizov, Aad Dijksma, and Stefania A. M. Marcantognini, On commutant lifting with finite defect. II, J. Funct. Anal. 144 (1997), no. 1, 105–116. MR 1430717
J. A. Ball and V. Bolotnikov, de Branges-Rovnyak spaces: basics and theory, Operator theory (D. Alpay, ed.), Springer, Basel, 2015, pp. 631–679.
Louis de Branges and James Rovnyak, Canonical models in quantum scattering theory, Perturbation Theory and its Applications in Quantum Mechanics (Proc. Adv. Sem. Math. Res. Center, U.S. Army, Theoret. Chem. Inst., Univ. of Wisconsin, Madison, Wis., 1965), Wiley, New York, 1966, pp. 295–392. MR 0244795
——, Square summable power series, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1966. MR 0215065
Emmanuel Fricain and Javad Mashreghi, The theory of\(\mathcal H\)(b) spaces. Vol. 1, New Mathematical Monographs, vol. 20, Cambridge University Press, Cambridge, 2016. MR 3497010
——, The theory of\(\mathcal {H}(b)\)spaces. Vol. 2, New Mathematical Monographs, vol. 21, Cambridge University Press, Cambridge, 2016. MR 3617311
Stephan Ramon Garcia, Javad Mashreghi, and William T. Ross, Introduction to model spaces and their operators, Cambridge Studies in Advanced Mathematics, vol. 148, Cambridge University Press, Cambridge, 2016. MR 3526203
N. K. Nikol\('\)skiı̆, Treatise on the shift operator, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 273, Springer-Verlag, Berlin, 1986, Spectral function theory, With an appendix by S. V. Hruščev [S. V. Khrushchëv] and V. V. Peller, Translated from the Russian by Jaak Peetre. MR 827223
Donald Sarason, Generalized interpolation in\(H^{\infty }\), Trans. Amer. Math. Soc. 127 (1967), 179–203. MR 208383
——, Shift-invariant spaces from the Brangesian point of view, The Bieberbach conjecture (West Lafayette, Ind., 1985), Math. Surveys Monogr., vol. 21, Amer. Math. Soc., Providence, RI, 1986, pp. 153–166. MR 875239
——, Sub-Hardy Hilbert spaces in the unit disk, University of Arkansas Lecture Notes in the Mathematical Sciences, vol. 10, John Wiley & Sons, Inc., New York, 1994, A Wiley-Interscience Publication. MR 1289670
Morris Schreiber, A functional calculus for general operators in Hilbert space, Trans. Amer. Math. Soc. 87 (1958), 108–118. MR 99601
Béla Sz.-Nagy and Ciprian Foiaş, Sur les contractions de l’espace de Hilbert. III, Acta Sci. Math. (Szeged) 19 (1958), 26–45. MR 103418
——, Harmonic analysis of operators on Hilbert space, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970, Translated from the French and revised. MR 0275190
Dan Timotin, A short introduction to de Branges–Rovnyak spaces, Invariant subspaces of the shift operator, Contemp. Math., vol. 638, Amer. Math. Soc., Providence, RI, 2015, pp. 21–38. MR 3309347
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Rovnyak, J. (2023). An Indefinite Analog of Sarason’s Generalized Interpolation Theorem. In: Binder, I., Kinzebulatov, D., Mashreghi, J. (eds) Function Spaces, Theory and Applications. Fields Institute Communications, vol 87. Springer, Cham. https://doi.org/10.1007/978-3-031-39270-2_2
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