References
D. Alpay, Some Krein spaces of analytic functions and an inverse scattering problem. Michigan Math. J.34, 349–359 (1987).
D.Alpay, Some remarks on reproducing kernel Krein spaces. To appear in Rocky Mountain J. Math.
D.Alpay, Some reproducing kernel spaces of continuous functions. To appear in J. Math. Anal. Appl.
D.Alpay, A Theorem on reproducing kernel Hilbert spaces of pairs. To appear in Rocky Mountain J. Math.
D.Alpay, P.Bruinsma, A.Dijksma and H.de Snoo, Interpolation problems, extension of symmetric operators and reproducing kernel spaces II. To appear in J. Integral Equations Operation Theory.
D. Alpay andH. Dym, On applications of reproducing kernel spaces to the Schur algorithm and rationalJ-unitary factorization. Oper. Theory: Adv. Appl.18, 89–159 (1986).
D. Alpay andH. Dym, Structured invariant spaces of vector valued functions, sesquilinear forms and a generalization of the lohvidov laws. Linear Algebra Appl.137, 413–451 (1991).
R. Arocena, A Theorem of Naimark, linear Systems and scattering operators. J. Funct. Anal.69, 281–288 (1986).
N. Aronszajn, Theory of reproducing kernels. Trans. Amer. Math. Soc.68, 337–404 (1950).
Y. Bistritz, H. Lev-Ari andT. Kailath, Immittance versus Scattering-Domain Fast Algorithms for non-Hermitian Toeplitz and quasi-Toeplitz Matrices. Linear Algebra Appl.122/123/124, 847–888 (1989).
L.de Branges, Hilbert spaces of entire functions. Englewoods Cills, N.J. 1968.
L. De Branges, Krein spaces of analytic functions. J. Funct. Anal.81, 219–259 (1988).
L.de Branges, A construction of Krein spaces of analytic functions. To appear in J. Funct. Anal.
L.de Branges and J.Rovnyak, Square summable power series. New York 1966.
M. Cotlar andC. Sadoski, Integral representations of bounded Hankel forms defined in scattering systems with a multiparametric evolution group. Oper. Theory: Adv. Appl.35, 357–375 (1988).
H. Dym,J-contractive matrix functions, reproducing kernel Hilbert spaces and interpolation. CBMS Lecture Notes71, Amer. Math. Soc., Providence, R.I. 1989.
L. Schwartz, Sous espaces Hilbertiens d'espaces vectoriels topologiques et noyaux associés (noyaux reproduisants), J. Analyse Math.13, 115–256 (1964).
A. M.Yang, A construction of Krein spaces of analytic functions. Ph.D. thesis, Purdue University, 1990.
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Alpay, D. On linear combinations of positive functions, associated reproducing kernel spaces and a non hermitian Schur algorithm. Arch. Math 58, 174–182 (1992). https://doi.org/10.1007/BF01191883
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DOI: https://doi.org/10.1007/BF01191883