SELECTED WORKS

Current interests in Kreĭn space operator theory

• M. A. Dritschel, A. Maestripieri, and J. Rovnyak, Hermitian indices and factorization of selfadjoint operators on a Kreĭn space, Submitted, 2026.
• M. A. Dritschel, A. Maestripieri, and J. Rovnyak, Rearrangement Invariant Orthogonal Sums in Kreĭn Spaces. II. Complex Anal. Oper. Theory 20, 64 (2026).
• J. Rovnyak, Rearrangement Invariant Orthogonal Sums in Kreĭn Spaces. I. Complex Anal. Oper. Theory 19, 148 (2025).
• J. Rovnyak, An indefinite analog of Sarason's generalized interpolation theorem, in Function Spaces, Theory and Applications, I. Binder et al. (eds.), Fields Institute Communications 87, pp. 25--57, 2023.
• J. Rovnyak, Orthogonal sums in Kreĭn spaces, Proc. Amer. Math. Soc. 149 (2021), no. 5, 1999-2010.
• D. Alpay, A. Dijksma, and J. Rovnyak, On Nudel'man's problem and indefinite interpolation in the generalized Schur and Nevanlinna classes, Complex Analysis and Operator Theory 14 (2020), no. 1, 30 pp.
• D. Alpay, A. Dijksma, and J. Rovnyak, Corrigendum to "Notes on interpolation in the generalized Schur class. II. Nudel'man's problem, Trans. Amer. Math. Soc. 371 (2019), no. 5, 3743-3745.
• D. Z. Arov, J. Rovnyak, and S. M. Saprikin, Linear passive stationary scattering systems with Pontryagin state spaces, Math. Nachr. 279 (2006), no. 13--14, 1396--1424.
• D. Alpay, A. Dijksma, and J. Rovnyak, A theorem of Beurling-Lax type for Hilbert spaces of functions analytic in the unit ball, Integral Equations Operator Theory 47 (2003), 251-274.
• D. Alpay, V. Bolotnikov, A. Dijksma, and J. Rovnyak, Some extensions of Loewner's theory of monotone operator functions, J. Funct. Anal. (2002), no. 1, 1--20.
• J. Rovnyak, Methods of Kreĭn space operator theory, Oper. Theory Adv. Appl. 134, Birkhauser, Basel, 2002, pp. 31-66.
• D. Alpay and J. Rovnyak, Loewner's theorem for kernels having a finite number of negative squares, Proc. Amer. Math. Soc. 127 (1999), no. 4, 1109--1117.
• D. Alpay, A. Dijksma, J. Rovnyak, and H. S. V. de Snoo, Reproducing kernel Pontryagin spaces, Holomorphic Spaces, Math. Sci. Res. Inst. Publ., Vol. 33, Cambridge University Press, 1998, pp. 425-444.
• D. Alpay, A. Dijksma, J. Rovnyak, and H. S. V. de Snoo, Schur functions, operator colligations, and reproducing kernel Pontryagin spaces, Oper. Theory Adv. Appl. 96, Birkhauser, 1997.
• M. A. Dritschel and J. Rovnyak, Operators on indefinite inner product spaces, Fields Inst. Monogr., Vol. 3, Amer. Math. Soc., Providence, RI, 1996, pp. 141-232.
• G. Christner, K. Y. Li, and J. Rovnyak, Julia operators and coefficient problems, in Nonselfadjoint operators and related topics (Beer Sheva, 1992), Oper. Theory Adv. Appl. 73, Birkhauser 1994, pp.~138-181
• K. Y. Li and J. Rovnyak, On the coefficients of Riemann mappings of the unit disk into itself, Oper. Theory Adv. Appl. 62, Birkhauser, 1993.
• M. A. Dritschel and J. Rovnyak, Julia operators and complementation in Kreĭn spaces, Indiana Univ. Math. J. 40 (1991), 885-901.
• M. A. Dritschel and J. Rovnyak, Extension theorems for contraction operators on Kreĭn spaces, Oper. Theory Adv. Appl. 47, Birkhauser Verlag, Basel, 1990, pp. 221-305.
• J. Rovnyak,  Coefficient estimates for Riemann mapping functions, J. Analyse Math. 52 (1989), 53-93.

Other interests

• S. M. Rovnyak, E. K. P. Chong, and J. Rovnyak, First-Order Conditions for Set-Constrained Optimization, Mathematics 2023, 11, 4274.
• J. Rovnyak, Hilbert spaces of entire functions: early history, Operator Theory, Vol.~1, Edited by Daniel Alpay, Springer, Basel (2015), 473--487.
• M. R. Palmer, C. L. Suiter, G. E. Henry, J. Rovnyak, J. C. Hoch, T. Polenova, and D. Rovnyak, Sensitivity of nonuniform sampling NMR J. Phys. Chem. B, 119 (2015), 6502-6515.
• M. A. Dritschel and J. Rovnyak, The operator Fejér-Riesz theorem, Paul R. Halmos in Memorium, Oper. Theory Adv. Appl. 207 (2010), 223-254.
• J. M. Anderson, M. A. Dritschel, and J. Rovnyak, Schwarz-Pick inequalities for the Schur-Agler class on the polydisk and unit ball, Comput. Methods Funct. Theory 8 (2008), no. 1-2, 339-361.
• J. M. Anderson and J. Rovnyak, On generalized Schwarz-Pick estimates, Mathematika 53 (2006), 161-168.
• J. M. Anderson, J. G. Clunie, M. Rosenblum, and J. Rovnyak, Some problems of best approximation with constraints, J. Approx. Theory 52 (1988), no. 1, 82--106; MR0922595.
• C. Markett, M. Rosenblum and J. Rovnyak, A Plancherel theory for Newton spaces, Integral Equations Operator Theory 9 (1986), no. 6, 831--862; MR0866967.
• J. M. Anderson, M. Rosenblum and J. Rovnyak, Hilbert space extremal problems with constraints, J. London Math. Soc. (2) 31 (1985), no. 3, 517--525; MR0812781.

Joint papers with L. A. Sakhnovich on operator identities in interpolation and spectral theory

• On indefinite cases of operator identities which arise in interpolation theory. II Oper. Theory Adv. Appl. 244 (2015), 341-378.
• Pseudospectral functions for canonical differential systems. II Oper. Theory Adv. Appl. 218 (2012), 583-612.
• Pseudospectral functions for canonical differential systems The Mark Kreĭn Centenary Conference, Vol. 2, Oper. Theory Adv. Appl. 191 (2009), 187-219.
• Integral representations for generalized difference kernels having a finite number of negative squares, Integral Equations Operator Theory, 63 (2009), no. 2, 281--296.
• Inverse problems for canonical differential equations with singularities, Oper. Theory Adv. Appl. 179 (2007), 257--288.
• Interpolation problems for matrix integro-differential operators with difference kernels and with a finite number of negative squares,Tiberiu Constantinescu Memorial Volume, Theta Foundation, Bucharest, 2007, 325--340.
• On indefinite cases of operator identities which arise in interpolation theory, Oper. Theory Adv. Appl. 171 (2006), 281-322.
• Spectral problems for some indefinite cases of canonical differential equations. J. Operator Theory 51 (2004), no. 1, 115-139.
• On the Kreĭn-Langer integral representation of generalized Nevanlinna functions, Electronic Journal of Linear Algebra 11 (2004), 1-15.
• Some indefinite cases of spectral problems for canonical systems of difference equations, Linear Algebra Appl. 343/344 (2002), 267-289.

Rosenblum-Rovnyak books and papers on operator theory and analysis

• Topics in Hardy classes and univalent functions}, Birkhäuser Advanced Texts: Basler Lehrbücher, Birkhäuser, Basel, 1994; MR1307384.
• Hardy classes and operator theory, Oxford Mathematical Monographs Oxford Science Publications, Oxford Univ. Press, New York, 1985; MR0822228.
• An operator-theoretic approach to theorems of the Pick-Nevanlinna and Loewner types. II, Integral Equations Operator Theory 5 (1982), no. 6, 870--887; MR0682304.
• An operator-theoretic approach to theorems of the Pick-Nevanlinna and Loewner types. I, Integral Equations Operator Theory 3 (1980), no. 3, 408--436; MR0580716.
• Change of variables formulas with Cayley inner functions, in Topics in functional analysis (essays dedicated to M. G. Kreĭn on the occasion of his 70th birthday), pp. 283--320, Adv. Math. Suppl. Stud., 3, Academic Press, New York-London; MR0538025.
• Cayley inner functions and best approximation, J. Approximation Theory 17 (1976), no. 3, 241--253; MR0613986.
• Restrictions of analytic functions. III, Proc. Amer. Math. Soc. 52 (1975), 222--226; MR0399926.
• Restrictions of analytic functions. II, Proc. Amer. Math. Soc. 51 (1975), 335--343; MR0399925.
• Restrictions of analytic functions. I, Proc. Amer. Math. Soc. 48 (1975), 113--119; MR0399924.
• Two theorems on finite Hilbert transforms, J. Math. Anal. Appl. 48 (1974), 708--720; MR0365006.
• An algebraic approach to the factorization problem for non-negative Toeplitz operators, Indiana Univ. Math. J. 20 (1971), no. 10, 939--940; MR0636335.
• The factorization problem for nonnegative operator valued functions, Bull. Amer. Math. Soc. 77 (1971), 287--318; MR0273437.
• Factorization of operator valued entire functions, Indiana Univ. Math. J. 20 (1970/71), 157--173; MR0261390.
• Factorization of operator valued entire functions, Bull. Amer. Math. Soc. 75 (1969), 1343--1346; MR0250108.

Invariant subspaces and the canonical model

• J. Rovnyak and V. Rovnyak, Sonine spaces on entire functions, J. Math. Anal. Appl. 27 (1969), 68-100; MR0243333.
• J. Rovnyak and V. Rovnyak, Self-reciprocal functions for the Hankel transformation of integer order Rovnyak, Duke Math. J. 34 (1967), 771-785; MR0218846.
• L. de Branges and J. Rovnyak, Canonical models in quantum scattering theory, Perturbation Theory and its Applications in Quantum Mechanics, Wiley, 1966, pp. 295-392
• L. de Branges and J. Rovnyak, Square summable power series, Holt, Rinehart, and Winston, New York, 1966
• J. Rovnyak, Ideals of square summable power series. II, Proc. Amer. Math. Soc. 16 (1965), 209-212; MR0173143.
• L. de Branges and J. Rovnyak, The existence of invariant subspaces, Bull. Amer. Math. Soc. 70 (1964), 718-721; retraction, ibid. 71 (1965), 396.
• J. Rovnyak, Ideals of square summable power series, Proc. Amer. Math. Soc. 13 (1962), 360-365; MR0139015.

Other accounts:

• J. A. Ball and V. Bolotnikov, de Branges-Rovnyak spaces: basics and theory, Operator Theory, Vol.~1, 631-679, Edited by Daniel Alpay, Springer, Basel (2015); de Branges-Rovnyak spaces and norm-constrained interpolation, ibid. 681-720.
• E. Fricain and J. Mashreghi, The theory of H(b) spaces, Vols. 1, 2, Cambridge University Press, 2016.

Unpublished papers

• J. Rovnyak, An extension problem for the coefficients of Riemann mappings, University of Virginia seminar lecture, November 1991. The topic of the lecture is a theorem of L. de Branges on the Taylor coefficients of a univalent function. The lecture is an exposition of an elegant result that I learned from a book draft that L. de Branges circulated in the 1980s (unpublished); the result is quoted without proof as Theorem 1.2 in J. Rovnyak, Coefficient estimates for Riemann mapping functions, J. Analyse Math. 52 (1989), 53-93. V. I. Vasyunin and N. K. Nikolskii prove the result in pp. 1219-1225 of their paper, Operator-valued measures and coefficients of univalent functions, St. Petersburg Math. J. 3 (1992), pp. 1199-1270; statements by these authors on pp. 1203, 1219 cast doubt on the completeness of the original proof of de Branges. I believe the original proof of de Branges is complete and correct, and my lecture fleshes out the details.
• J. Rovnyak, Characterization of spaces H(M), Unpublished paper, 1968; cited by D. Z. Arov and H. Dym in  J-Contractive Matrix Valued Functions and Related Topics, Cambridge University Press, 2008, pp. 254, 332.