Bulletin of the American Mathematical Society

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Book Information:

Authors: Emmanuel Fricain and Javad Mashreghi
Title: The theory of $\mathcal {H}(b)$ spaces, Vol. 1
Additional book information: New Mathematical Monographs, Vol. 20, Cambridge University Press, Cambridge, 2016, xix+681 pp., ISBN 978-1-107-02777-0

Authors: Emmanuel Fricain and Javad Mashreghi
Title: The theory of $\mathcal {H}(b)$ spaces, Vol. 2
Additional book information: New Mathematical Monographs, Vol. 21, Cambridge University Press, Cambridge, 2016, xix+619 pp., ISBN 978-1-107-02778-7

J. M. Anderson and J. Rovnyak, On generalized Schwarz-Pick estimates, Mathematika 53 (2006), no. 1, 161–168 (2007). MR 2304058, DOI 10.1112/S0025579300000085

J. A. Ball and V. Bolotnikov, de Branges-Rovnyak Spaces: Basics and Theory (2014), available at https://arxiv.org/abs/1405.2980v1.

Joseph A. Ball and Thomas L. Kriete III, Operator-valued Nevanlinna-Pick kernels and the functional models for contraction operators, Integral Equations Operator Theory 10 (1987), no. 1, 17–61. MR 868573, DOI 10.1007/BF01199793

Anton Baranov, Emmanuel Fricain, and Javad Mashreghi, Weighted norm inequalities for de Branges-Rovnyak spaces and their applications, Amer. J. Math. 132 (2010), no. 1, 125–155. MR 2597508, DOI 10.1353/ajm.0.0094

Arne Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 239–255. MR 27954, DOI 10.1007/BF02395019

Alain Blandignères, Emmanuel Fricain, Frédéric Gaunard, Andreas Hartmann, and William T. Ross, Direct and reverse Carleson measures for $\mathcal H(b)$ spaces, Indiana Univ. Math. J. 64 (2015), no. 4, 1027–1057. MR 3385785, DOI 10.1512/iumj.2015.64.5604

Vladimir Bolotnikov and Alexander Kheifets, A higher order analogue of the Carathéodory-Julia theorem, J. Funct. Anal. 237 (2006), no. 1, 350–371. MR 2239269, DOI 10.1016/j.jfa.2006.03.016

Arlen Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/64), 89–102. MR 160136, DOI 10.1007/978-1-4613-8208-9_{1}9

Nicolas Chevrot, Dominique Guillot, and Thomas Ransford, De Branges-Rovnyak spaces and Dirichlet spaces, J. Funct. Anal. 259 (2010), no. 9, 2366–2383. MR 2674117, DOI 10.1016/j.jfa.2010.07.004

Constantin Costara and Thomas Ransford, Which de Branges-Rovnyak spaces are Dirichlet spaces (and vice versa)?, J. Funct. Anal. 265 (2013), no. 12, 3204–3218. MR 3110499, DOI 10.1016/j.jfa.2013.08.015

R. Bruce Crofoot, Multipliers between invariant subspaces of the backward shift, Pacific J. Math. 166 (1994), no. 2, 225–246. MR 1313454

Louis de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), no. 1-2, 137–152. MR 772434, DOI 10.1007/BF02392821

Louis de Branges, Unitary linear systems whose transfer functions are Riemann mapping functions, Operator theory and systems (Amsterdam, 1985) Oper. Theory Adv. Appl., vol. 19, Birkhäuser, Basel, 1986, pp. 105–124. MR 903695

Louis de Branges, Underlying concepts in the proof of the Bieberbach conjecture, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 25–42. MR 934213

Louis de Branges and James Rovnyak, Square summable power series, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1966. MR 0215065

Karel de Leeuw and Walter Rudin, Extreme points and extremum problems in $H_{1}$, Pacific J. Math. 8 (1958), 467–485. MR 98981

B. Mark Davis and John E. McCarthy, Multipliers of de Branges spaces, Michigan Math. J. 38 (1991), no. 2, 225–240. MR 1098860, DOI 10.1307/mmj/1029004330

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, DOI 10.1017/CBO9781316258231

Andreas Hartmann, Donald Sarason, and Kristian Seip, Surjective Toeplitz operators, Acta Sci. Math. (Szeged) 70 (2004), no. 3-4, 609–621. MR 2107530

Benjamin A. Lotto, Inner multipliers of de Branges’s spaces, Integral Equations Operator Theory 13 (1990), no. 2, 216–230. MR 1038151, DOI 10.1007/BF01193757

N. K. Nikol′skiĭ, 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, DOI 10.1007/978-3-642-70151-1

Nikolai K. Nikolski, Operators, functions, and systems: an easy reading. Vol. 2, Mathematical Surveys and Monographs, vol. 93, American Mathematical Society, Providence, RI, 2002. Model operators and systems; Translated from the French by Andreas Hartmann and revised by the author. MR 1892647

Nikolai K. Nikolski, Operators, functions, and systems: an easy reading. Vol. 1, Mathematical Surveys and Monographs, vol. 92, American Mathematical Society, Providence, RI, 2002. Hardy, Hankel, and Toeplitz; Translated from the French by Andreas Hartmann. MR 1864396

N. K. Nikol′skiĭ and V. I. Vasyunin, Notes on two function models, The Bieberbach conjecture (West Lafayette, Ind., 1985) Math. Surveys Monogr., vol. 21, Amer. Math. Soc., Providence, RI, 1986, pp. 113–141. MR 875237, DOI 10.1090/surv/021/11

Donald Sarason, Exposed points in $H^1$. I, The Gohberg anniversary collection, Vol. II (Calgary, AB, 1988) Oper. Theory Adv. Appl., vol. 41, Birkhäuser, Basel, 1989, pp. 485–496. MR 1038352

Donald Sarason, Exposed points in $H^1$. II, Topics in operator theory: Ernst D. Hellinger memorial volume, Oper. Theory Adv. Appl., vol. 48, Birkhäuser, Basel, 1990, pp. 333–347. MR 1207406

Donald Sarason, 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

Donald Sarason, Local Dirichlet spaces as de Branges-Rovnyak spaces, Proc. Amer. Math. Soc. 125 (1997), no. 7, 2133–2139. MR 1396993, DOI 10.1090/S0002-9939-97-03896-3

Donald Sarason, Algebraic properties of truncated Toeplitz operators, Oper. Matrices 1 (2007), no. 4, 491–526. MR 2363975, DOI 10.7153/oam-01-29

Béla Sz.-Nagy and Ciprian Foiaş, 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

Béla Sz.-Nagy, Ciprian Foias, Hari Bercovici, and László Kérchy, Harmonic analysis of operators on Hilbert space, Revised and enlarged edition, Universitext, Springer, New York, 2010. MR 2760647, DOI 10.1007/978-1-4419-6094-8

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, DOI 10.1090/conm/638/12803

• J. M. Anderson and J. Rovnyak, On generalized Schwarz-Pick estimates, Mathematika 53 (2006), no. 1, 161–168 (2007). MR 2304058
• J. A. Ball and V. Bolotnikov, de Branges-Rovnyak Spaces: Basics and Theory (2014), available at https://arxiv.org/abs/1405.2980v1.
• Joseph A. Ball and Thomas L. Kriete III, Operator-valued Nevanlinna-Pick kernels and the functional models for contraction operators, Integral Equations Operator Theory 10 (1987), no. 1, 17–61. MR 868573
• Anton Baranov, Emmanuel Fricain, and Javad Mashreghi, Weighted norm inequalities for de Branges-Rovnyak spaces and their applications, Amer. J. Math. 132 (2010), no. 1, 125–155. MR 2597508
• Arne Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 17. MR 0027954
• Alain Blandignères, Emmanuel Fricain, Frédéric Gaunard, Andreas Hartmann, and William T. Ross, Direct and reverse Carleson measures for $\mathcal {H}(b)$ spaces, Indiana Univ. Math. J. 64 (2015), no. 4, 1027–1057. MR 3385785
• Vladimir Bolotnikov and Alexander Kheifets, A higher order analogue of the Carathéodory-Julia theorem, J. Funct. Anal. 237 (2006), no. 1, 350–371. MR 2239269
• Arlen Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/1964), 89–102. MR 0160136
• Nicolas Chevrot, Dominique Guillot, and Thomas Ransford, De Branges-Rovnyak spaces and Dirichlet spaces, J. Funct. Anal. 259 (2010), no. 9, 2366–2383. MR 2674117
• Constantin Costara and Thomas Ransford, Which de Branges-Rovnyak spaces are Dirichlet spaces (and vice versa)?, J. Funct. Anal. 265 (2013), no. 12, 3204–3218. MR 3110499
• R. Bruce Crofoot, Multipliers between invariant subspaces of the backward shift, Pacific J. Math. 166 (1994), no. 2, 225–246. MR 1313454
• Louis de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), no. 1-2, 137–152. MR 772434
• Louis de Branges, Unitary linear systems whose transfer functions are Riemann mapping functions, Operator theory and systems (Amsterdam, 1985) Oper. Theory Adv. Appl., vol. 19, Birkhäuser, Basel, 1986, pp. 105–124. MR 903695
• Louis de Branges, Underlying concepts in the proof of the Bieberbach conjecture, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 25–42. MR 934213
• Louis de Branges and James Rovnyak, Square summable power series, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1966. MR 0215065
• Karel de Leeuw and Walter Rudin, Extreme points and extremum problems in $H_{1}$, Pacific J. Math. 8 (1958), 467–485. MR 0098981
• B. Mark Davis and John E. McCarthy, Multipliers of de Branges spaces, Michigan Math. J. 38 (1991), no. 2, 225–240. MR 1098860
• 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
• Andreas Hartmann, Donald Sarason, and Kristian Seip, Surjective Toeplitz operators, Acta Sci. Math. (Szeged) 70 (2004), no. 3-4, 609–621. MR 2107530
• Benjamin A. Lotto, Inner multipliers of de Branges’s spaces, Integral Equations Operator Theory 13 (1990), no. 2, 216–230. MR 1038151
• N. K. Nikol′skiĭ, 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
• Nikolai K. Nikolski, Operators, functions, and systems: an easy reading. Vol. 2, Mathematical Surveys and Monographs, vol. 93, American Mathematical Society, Providence, RI, 2002. Model operators and systems; Translated from the French by Andreas Hartmann and revised by the author. MR 1892647
• Nikolai K. Nikolski, Operators, functions, and systems: an easy reading. Vol. 1, Mathematical Surveys and Monographs, vol. 92, American Mathematical Society, Providence, RI, 2002. Hardy, Hankel, and Toeplitz; Translated from the French by Andreas Hartmann. MR 1864396
• N. K. Nikol′skiĭand V. I. Vasyunin, Notes on two function models, The Bieberbach conjecture (West Lafayette, Ind., 1985) Math. Surveys Monogr., vol. 21, Amer. Math. Soc., Providence, RI, 1986, pp. 113–141. MR 875237
• Donald Sarason, Exposed points in $H^1$. I, The Gohberg anniversary collection, Vol. II (Calgary, AB, 1988) Oper. Theory Adv. Appl., vol. 41, Birkhäuser, Basel, 1989, pp. 485–496. MR 1038352
• Donald Sarason, Exposed points in $H^1$. II, Topics in operator theory: Ernst D. Hellinger memorial volume, Oper. Theory Adv. Appl., vol. 48, Birkhäuser, Basel, 1990, pp. 333–347. MR 1207406
• Donald Sarason, 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
• Donald Sarason, Local Dirichlet spaces as de Branges-Rovnyak spaces, Proc. Amer. Math. Soc. 125 (1997), no. 7, 2133–2139. MR 1396993
• Donald Sarason, Algebraic properties of truncated Toeplitz operators, Oper. Matrices 1 (2007), no. 4, 491–526. MR 2363975
• Béla Sz.-Nagy and Ciprian Foiaş, Harmonic analysis of operators on Hilbert space, Translated from the French and revised, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970. MR 0275190
• Béla Sz.-Nagy, Ciprian Foias, Hari Bercovici, and László Kérchy, Harmonic analysis of operators on Hilbert space, Revised and enlarged edition, Universitext, Springer, New York, 2010. MR 2760647
• 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