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Bibliography [AA66] Vadim M. Adamjan and Damir Z. Arov, Unitary couplings of semi- unitary operators, (Russian) Mat. Issled. 1 (1966), no. 2, 3–64. [AA68] Vadim M. Adamjan and Damir Z. Arov, A general solution of a cer- tain problem in the linear prediction of stationary processes, (Rus- sian) Teor. Verojatnost. i Primenen. 13 (1968) 419–431; English translation: Theor. Probability Appl. 13 (1968), 394–407 [AAK71] Vadim M. Adamjan, Damir Z. Arov and Mark G. Krein, Analytic properties of Schmidt pairs of a Hankel operator and the generalized Schur–Takagi problem, (Russian) Mat. Sb. (N.S.) 86(128) (1971), 34– 75; English translation: Math USSR Sbornik 15 (1971), no. 1, 31–73. [AR68] Naum I. Ahiezer, and Alexander M. Rybalko, Continual analogues of polynomials orthogonal on a circle, (Russian) Ukrain.Mat.Z.20 (1968), no. 1, 3–24. [AlD84] Daniel Alpay and Harry Dym, Hilbert spaces of analytic functions, in- verse scattering and operator models, I., Integral Equations Operator Theory 7 (1984), no. 5, 589–641. [AlD85] Daniel Alpay and Harry Dym, Hilbert spaces of analytic functions, in- verse scattering and operator models, II., Integral Equations Operator Theory 8 (1985), no. 2, 145–180. [AlD93] Daniel Alpay and Harry Dym, On a new class of structured repro- ducing kernel spaces, J. Functional Analysis 111 (1993), no. 1, 1–28. [AlG95] Daniel Alpay and Israel Gohberg, Inverse spectral problem for differ- ential operators with rational scattering matrix functions, J. Differ- ential Equations 118 (1995), no. 1, 1–19. [AlG97] Daniel Alpay and Israel Gohberg, State space method for inverse spec- tral problems, in: Systems and Control in the Twenty-first Century (St. Louis, MO, 1996), Progr. Systems Control Theory 22, Birkh¨auser Boston, Boston, MA, 1997, pp. 1–16. [AlG01] Daniel Alpay and Israel Gohberg, Inverse problems associated to a canonical differential system, in: Recent Advances in Operator The- ory and Related Topics (Szeged, 1999), Operator Theory: Advances Applications 127, Birkh¨auser, Basel, 2001, pp. 1–27. © Springer International Publishing AG, part of Springer Nature 2018 385 D. Z. Arov, H. Dym, Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems, Operator Theory: Advances and Applications 266, https://doi.org/10.1007/978-3-319-70262-9 386 Bibliography [AGKS00] Daniel Alpay, Israel Gohberg, Marinus A. Kaashoek, Leonid Lerer and Alexander Sakhnovich, Direct and inverse scattering problem for canonical systems with a strictly pseudo-exponential potential, Math. Nachr. 215 (2000), 5–31. (Reviewer: Hendrik S. V. de Snoo) [AGKLS09] Daniel Alpay, Israel Gohberg, Marinus A. Kaashoek, Leonid Lerer and Alexander Sakhnovich, Krein systems, in: Modern Analysis and Applications. The Mark Krein Centenary Conference. Vol. 2: Differ- ential operators and mechanics, Operator Theory: Advances Applica- tions 191, Birkh¨auser, Basel, 2009, pp. 19–36. [AGKLS10] Daniel Alpay, Israel Gohberg, Marinus A. Kaashoek, Leonid Lerer and Alexander L. Sakhnovich, Krein systems and canonical systems on a finite interval: accelerants with a jump discontinuity at the origin and continuous potentials, Integral Equations Operator Theory 68 (2010), no. 1, 115–150. [Arn50] Nachman Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337–404. [Ar74] Damir Z. Arov, Scattering theory with dissipation of energy, (Rus- sian) Dokl. Akad. Nauk SSSR 216 (1974), 713–716; English transla- tion: Soviet Math. Dokl. 15 (1974), 848–854. [Ar79a] Damir Z. Arov, Optimal and stable passive systems, (Russian) Dokl. Akad Nauk SSSR 247 (1979 ), no. 2, 265–268; English translation: Soviet Math. Dokl. 20 (1979), no. 4, 676–680. [Ar79b] Damir Z. Arov, Passive linear steady-state dynamical systems, (Rus- sian) Sibirsk. Mat. Zh. 20 (1979), no. 2, 211–228; English translation: Siberian Math. J. 20 (1979), no. 2, 149–162. [Ar90] Damir Z. Arov, Regular J-inner matrix-functions and related contin- uation problems, in: Linear Operators in Function Spaces (Timi¸soara, 1988), Operator Theory: Advances Applications 43, Birkh¨auser, Basel, 1990, pp. 63–87. [Ar93] Damir Z. Arov, The generalized bitangent Carath´eodory–Nevanlinna- Pick problem and (j, J0)-inner matrix functions, (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 57 (1993), no. 1, 3–32; English translation: Russian Acad. Sci. Izv. Math. 42 (1994), no. 1, 1–26. [ArD98] Damir Z. Arov and Harry Dym, On three Krein extension prob- lems and some generalizations, Integral Equations Operator Theory 31 (1998), no. 1, 1–91. [ArD02] Damir Z. Arov and Harry Dym, J-inner matrix functions, interpola- tion and inverse problems for canonical systems, V. The inverse input scattering problem for Wiener class and rational p × q input scatter- ing matrices, Integral Equations Operator Theory 43 (2002), no. 1, 68–129. Bibliography 387 [ArD05b] Damir Z. Arov and Harry Dym, Strongly regular J-inner matrix- valued functions and inverse problems for canonical systems, in: Recent Advances in Operator Theory and its Applications (M.A. Kaashoek, S. Seatzu and C. van der Mee, eds.), Operator Theory: Advances Applications 160, Birkh¨auser, Basel, 2005, pp. 101–160. [ArD05c] Damir Z. Arov and Harry Dym, Direct and inverse problems for differ- ential systems connected with Dirac systems and related factorization problems, Indiana Univ. Math. J. 54 (2005), no. 6, 1769–1815. [ArD07] Damir Z. Arov and Harry Dym, Direct and inverse asymptotic scattering problems for Dirac–Krein systems, (Russian) Funktsional. Anal. i Prilozhen. 41 (2007), no. 3, 17–33; English translation: Func- tional Anal. Appl. 41 (2007), no. 3, 181–195. [ArD07b] Damir Z. Arov and Harry Dym, Bitangential direct and inverse prob- lems for systems of differential equations, in: Probability, geometry and integrable systems (M. Pinsky and B. Birnir, eds.) Math. Sci. Res. Inst. Publ. 55, Cambridge University Press, Cambridge, 2008, pp. 1–28. [ArD08] Damir Z. Arov and Harry Dym, J-contractive Matrix Valued Func- tions and Related Topics, Encyclopedia of Mathematics and its Ap- plications 116, Cambridge University Press, Cambridge, 2008. [ArD12] Damir Z. Arov and Harry Dym, Bitangential Direct and Inverse Prob- lems for Systems of Integral and Differential Equations, Encyclope- dia of Mathematics and its Applications 145, Cambridge University Press, Cambridge, 2012. [ArK81] Damir Z. Arov and Mark G. Krein, The problem of finding the min- imum entropy in indeterminate problems of continuation, (Russian) Funktsional. Anal. i Prilozhen. 15 (1981), no. 2, 61–64; English trans- lation: Functional Anal. Appl. 1 15 (1981), no. 2, 123–126. [ArK83] Damir Z. Arov and Mark G. Krein, Calculation of entropy functionals and their minima in indeterminate continuation problems, (Russian) Acta Sci. Math. (Szeged) 45 (1983), no. 1–4, 33–50. [ArN96] Damir Z. Arov and Mark A. Nudelman, Passive linear stationary dy- namical scattering systems with continuous time, Integral Equations Operator Theory 24 (1996), no. 1, 1–45. [ArN02] Damir Z. Arov and Mark A. Nudelman, Conditions for the similarity of all minimal passive realizations of a given transfer function (scat- tering and resistance matrices), (Russian) Mat. Sb. 193 (2002), no. 6, 3–24; English translation Sb. Math. 193 (2002), no. 5–6, 791–810. [AS17] DamirZ.ArovandOlofJ.Staffans,Linear Stationary In- put/State/Output and State/Signal Systems, preprint available at http://users.abo.fi/staffans 388 Bibliography [ArR12] Damir Z. Arov and Natalia A. Rozhenko, Realizations of stationary stochastic processes: applications of passive system theory, Methods Functional Anal. Topology 18 (2012), no. 4, 305–331. [Art84] A.P. Artemenko, Hermitian positive functions and positive function- als, I, II, (Russian) Teor.FunktsiiFunktsional.Anal.iPrilhozen.41 (1984), 3–16; 42 (1984), 3–21. [BKSZ15] Joseph A. Ball, Mikael Kurula, Olof J. Staffans and Hans Zwart, De Branges–Rovnyak realizations of operator-valued Schur functions on the complex right half-plane, Complex Anal. Oper. Theory 9 (2015), no. 4, 723–792. [BG002] Laurent Baratchart, Andrea Gombani and Martine Olivi, Parameter determination for surface acoustic wave filters, in: Proceedings of the 39th IEEE Conference on Decision and Control (Sydney, Australia, 2000), 2002, pp. 2011–2016. [BEGO07] Laurent Baratchart, Per Enqvist, Andrea Gombani and Martine Olivi, Minimal symmetric Darlington synthesis, Math. Control Sig- nals Systems 19 (2007), no. 4, 283–311. [BGK82] Harm Bart, Israel Gohberg and Marinus A. Kaashoek, Convolution equations and linear systems, Integral Equations Operator Theory 5 (1982), no. 3, 283–340. [B12] Nicholas H. Bingham, Multivariate prediction and matrix Szeg˝othe- ory, Probab. Surv. 9 (2012), 325–339. [Br59] Louis de Branges, Some Hilbert spaces of entire functions, Proc. Amer. Math. Soc. 10 (1959), 840–846. [Br60] Louis de Branges, Some Hilbert spaces of entire functions, Trans. Amer. Math. Soc. 96 (1960), 259–295. [Br61a] Louis de Branges, Some Hilbert spaces of entire functions. II, Trans. Amer. Math. Soc. 99 (1961), 118–152. [Br61b] Louis de Branges, Some Hilbert spaces of entire functions. III, Trans. Amer. Math. Soc. 100 (1961), 73–115. [Br61c] Louis de Branges, Some Hilbert spaces of entire functions, Bull. Amer. Math. Soc. 67 (1961) 129–134. [Br62] Louis de Branges, Some Hilbert spaces of entire functions. IV, Trans. Amer. Math. Soc. 105 (1962), 43–83. [Br63] Louis de Branges, Some Hilbert spaces of analytic functions I, Trans. Amer. Math. Soc. 106 (1963), 445–468. [Br65] Louis de Branges, Some Hilbert spaces of analytic functions II, J. Math. Anal. Appl. 11 (1965), 44–72. [Br68a] Louis de Branges, Hilbert Spaces of Entire Functions. Prentice-Hall, Englewood Cliffs, 1968. Bibliography 389 [Br68b] Louis de Branges, The expansion theorem for Hilbert spaces of en- tire functions, in: Entire Functions and Related Parts of Analysis, Proc. Sympos. Pure Math. (La Jolla, Calif., 1966), Amer. Math. Soc., Providence, 1968, pp. 79–148. [Br83] Louis de Branges, The comparison theorem for Hilbert spaces of entire functions, Integral Equations Operator Theory 6 (1983), no. 5, 603– 646. [CP93] Raymond Cheng and Mohsen Pourahmadi, Baxter’s inequality and convergence of finite predictors of multivariate stochastic processes, Probab.
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  • Interview with Joseph Keller

    Interview with Joseph Keller

    Interview with Joseph Keller he moved to Stanford University, where he is now an emeritus professor. Keller has received many awards and honors throughout his career, including the von Karman Prize of the Society for Industrial and Applied Mathematics (1979), the Timoshenko Medal of the American Society of Mechanical Engineers (1984), the National Medal of Science (1988), the National Academy of Sciences Award in Applied Mathe- matics and Numerical Analysis (1995), the Nemmers Joe Keller at home in Stanford, CA. Prize from Northwestern University (1996), and Joseph B. Keller is one of the premier applied math- the Wolf Prize (1997). ematicians of recent times. The problems he has What follows is the edited text of an interview worked on span a wide range of areas, including with Keller conducted in March 2004 by Notices se- wave propagation, semiclassical mechanics, geo- nior writer and deputy editor Allyn Jackson. physical fluid dynamics, epidemiology, biome- chanics, operations research, finance, and the math- Early Years ematics of sports. His best-known work includes Notices: How did you get interested in mathemat- the Geometrical Theory of Diffraction, which is an ics? extension of the classical theory of optics and in- Keller: I was always good at mathematics as a spired the introduction of geometric methods in child. My father, who was not educated but was a the study of partial differential equations, and the smart guy, used to give my Einstein-Brillouin-Keller Method, which provided brother and me mathematical new ways to compute eigenvalues in quantum me- puzzles when we were kids. chanics. Keller has had about fifty doctoral students Here’s an example.