Geodesic
Blaschke product for a~Hilbert space with Schwarz--Pick kernel
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 43, Tome 434 (2015), pp. 68-81

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For an analog of a Blaschke product for a Hilbert space with Schwarz–Pick kernel (this is a wider class than the class of Hilbert spaces with Nevanlinna–Pick kernel), it is proved that only finitely many elementary multipliers may have zeros on a fixed compact set. It is proved also that the partial Blaschke products multiplied by an appropriate reproducing kernel converge in the Hilbert space. These abstract theorems are applied to the weighted Hardy spaces in the unit disk and to the Drury–Arveson spaces. 
@article{ZNSL_2015_434_a5,
     author = {I. V. Videnskii},
     title = {Blaschke product for {a~Hilbert} space with {Schwarz--Pick} kernel},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {68--81},
     publisher = {mathdoc},
     volume = {434},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a5/}
}
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I. V. Videnskii. Blaschke product for a~Hilbert space with Schwarz--Pick kernel. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 43, Tome 434 (2015), pp. 68-81. http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a5/