Geodesic
An analog of the hyperbolic metric generated by Hilbert space with Schwarz–Pick kernel
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 44, Tome 447 (2016), pp. 20-32
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It is proved that a Hilbert function space on the set $X$ with Schwarz–Pick kernel (this is a wider class than the class of Hilbert spaces with Nevanlinna–Pick kernel) generates the metric on the set $X$ – an analog of the hyperbolic metric in the unit disk. For a sequence satisfying an abstract Blaschke condition, it is proved that the associated infinite Blaschke product converges uniformly on any fixed bounded set and in the strong operator topology of the multiplier space. 
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I. V. Videnskii. An analog of the hyperbolic metric generated by Hilbert space with Schwarz–Pick kernel. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 44, Tome 447 (2016), pp. 20-32. http://geodesic.mathdoc.fr/item/ZNSL_2016_447_a1/

[1] J. Agler, J. E. McCarthy, Pick Interpolation and Hilbert Function Spaces, Graduate Studies in Mathematics, 44, Amer. Math. Soc., Providence, R.I., 2002 | DOI | MR | Zbl

[2] A. Aleman, The Multiplication Operators on Hilbert Spaces of Analytic Functions, Habilitationsschrift, Hagen, 1993

[3] D. E. Marshall, C. Sundberg, Interpolating sequences for the multipliers of the Dirichlet space, Preprint, Available at , 1993 http://www.math.washington.edu/~marshall/preprints/preprints.html

[4] K. Seip, Interpolation and Sampling in Spaces of analytic Functions, University lecture series, 33, Amer. Math. Soc., Providence, R.I., 2004 | DOI | MR | Zbl

[5] S. Shimorin, “Complete Nevanlinna–Pick property of Dirichlet-type spaces”, J. Funct. Anal., 191 (2002), 276–290 | DOI | MR

[6] S. M. Shimorin, “Vosproizvodyaschie yadra i ekstremalnye funktsii v prostranstvakh tipa Dirikhle”, Zap. nauchn. semin. POMI, 255, 1998, 198–220 | MR | Zbl

[7] I. V. Videnskii, “Ob analoge proizvedeniya Blyashke dlya gilbertova prostranstva s yadrom Nevanlinny–Pika”, Zap. nauchn. semin. POMI, 424, 2014, 126–140

[8] I. V. Videnskii, “Proizvedenie Blyashke dlya gilbertova prostranstva s yadrom Shvartsa–Pika”, Zap. nauchn. semin. POMI, 434, 2015, 68–81