A Noneuclidean Lax-Beurling Theorem with Applications to Matricial Nevanlinna-Pick Interpolation

Adamjan, V. M.; Arov, D.Z.; Krein, M. G., Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem, Math. USSR Sb. 15 (1971), 31–73.CrossRefGoogle Scholar

Adamjan, V. M.; Arov, D. Z.; Krein, M. G., Infinite Hankel block matrices and related extension problems, Amer. Math. Soc. Transl. (2)111 (1978), 133–156.Google Scholar

Arsene, G; Ceausescu, Z.; Foias, C., On intertwining dilations VIII, J. Operator Theory 4 (1980), 55–91.Google Scholar

Ball, J., Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions, preprint.Google Scholar

Ball, J; Helton, J. W., Lie groups over the field of rational functions, signed spectral factorization, signed interpolation, and amplifier design, preprint.Google Scholar

Ball, J; Helton, J. W., A Lax-Beurling theorem for the Lie group U(m,n) which contains most classical interpolation theory, preprint.Google Scholar

Bognár, J., Indefinite Inner Product Spaces, Springer-Verlag (1974).Google Scholar

Carathéodory, C; Fejér, L., Über den Zusammenhang der Extremen von harmonischen Funktionen mit ihrer Koeffizienten and über der Picard-Landauschen Satz, Rend. Cire. mat. Palermo, II Ser., 32 (1911), 218–239.CrossRefGoogle Scholar

Halmos, P., Shifts on Hilbert spaces, J. reine angew. Math., 209 (1961), 102–112.Google Scholar

Helton, J. W., Orbit structure of the Möbius transformation semigroup acting on H (broadband matching), Topics in Functional Analysis, Adv. in Math. Suppl. Studies 3, 129–157, Academic Press (1978).Google Scholar

Helton, J. W., The distance of a function to H^∞ in the Poincaré metric; electrical power transfer, J. Funct. Anal. 38 (1980), 273–314.CrossRefGoogle Scholar

Krein, M. G.; Langer, H., Über die verallgemeinerten Resolventen und die charakteristische Funktion eines isometrischen Operators im Raume Π_κ, Colloquia Mathematica Societatis Janos Bolyai 5, 353–399, North-Holland (1972).Google Scholar

McEnnis, B., Shifts on indefinite inner product spaces, Pac. J. Math., 81 (1979), 113–130.CrossRefGoogle Scholar

Sz.-Nagy, B; Foias, C., Dilations des commutants d’operateurs, C. R. Acad. Sci. Paris Sér. A, 266 (1968), 493–495.Google Scholar

Sz.-Nagy, B; Koranyi, A., Relations d’un probleme de Nevanlinna et Pick avec 1a theorie des Operateurs de l’espace Hilbertian, Acta Math. Acad. Sci. Hunger. 7 (1956), 295–302.CrossRefGoogle Scholar

Nehari, Z., On bounded bilinear forms, Ann. of Math., 65 (1957), 153–162.CrossRefGoogle Scholar

Nevanlinna, R., Über beschränkte Funktionen, die in gegebenen Punkten vorgeschriebene Werte annehmen, Ann. Acad. Sci. Fenn. 13:1 (1919).Google Scholar

Pick, G., Über die Beschränkungen analytischer Funktionen, welche durch vorgegebene Funktionswerte bewirkt sint, Math. Ann., 77 (1916), 7–23.CrossRefGoogle Scholar

Rosenblum, M.; Rovnyak, J., An operator-theoretic approach to theorems of the Pick-Nevanlinna and Loewner types I, Integral Equations and Operator Theory, 3 (1980), 408–436.CrossRefGoogle Scholar

Sarason, D., Generalized interpolation in H^∞, Trans. Amer. Math. Soc., 127 (1967), 179–203.Google Scholar

Schur, I., Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind, J. reine angew. Math., 148 (1918), 122–145.Google Scholar

Takagi, T., On an algebraic problem related to an analytic theorem of Carathéodory and Fejér, a) Japan J. Math. 1 (1924), 83–93; b) ibid. 2 (1925), 13-17.Google Scholar