On the zeros of the derivative of a~rational function and coinvariant subspaces for the shift operator on the Bergman space
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 29, Tome 282 (2001), pp. 26-33
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If all $n$ $(n>1)$ zeros of a rational function $r$ with simple poles are in a half-plane, then the derivative of $r$ has at least one zero in the same half-plane. This result is used to prove that the number of zeros of a linear combination of $n$ Bergman kernels in the unit disc may range from 0 to $2n-3$.
@article{ZNSL_2001_282_a2,
author = {I. V. Videnskii},
title = {On the zeros of the derivative of a~rational function and coinvariant subspaces for the shift operator on the {Bergman} space},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {26--33},
publisher = {mathdoc},
volume = {282},
year = {2001},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a2/}
}
TY - JOUR AU - I. V. Videnskii TI - On the zeros of the derivative of a~rational function and coinvariant subspaces for the shift operator on the Bergman space JO - Zapiski Nauchnykh Seminarov POMI PY - 2001 SP - 26 EP - 33 VL - 282 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a2/ LA - ru ID - ZNSL_2001_282_a2 ER -
%0 Journal Article %A I. V. Videnskii %T On the zeros of the derivative of a~rational function and coinvariant subspaces for the shift operator on the Bergman space %J Zapiski Nauchnykh Seminarov POMI %D 2001 %P 26-33 %V 282 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a2/ %G ru %F ZNSL_2001_282_a2
I. V. Videnskii. On the zeros of the derivative of a~rational function and coinvariant subspaces for the shift operator on the Bergman space. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 29, Tome 282 (2001), pp. 26-33. http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a2/