Geodesic
Multipoint Geronimus and Schur parameters of measures on a~circle and on a~line
Sbornik. Mathematics, Tome 215 (2024) no. 8, pp. 1007-1042

Voir la notice de l'article provenant de la source Math-Net.Ru

A theorem of Geronimus that a measure corresponding to a Carathéodory function with sufficiently small Schur parameters has a support coinciding with the whole unit circle is established in the multipoint version, when the points of interpolation of the continued fraction representing the Carathéodory function have a limit distribution (in Geronimus's classical theorem all points of interpolation are concentrated at the origin). The Geronimus and Schur parameters of measures with support on the real line are introduced. For measures with support on the real line and the corresponding Nevanlinna function it is shown that an analogue of Geronimus's theorem holds, as well as analogues of some other results on measures with support on the unit circle. Bibliography: 18 titles.
Keywords: continued fractions, orthogonal rational functions, Geronimus and Schur parameters, Carathéodory and Nevanlinna functions. 
@article{SM_2024_215_8_a0,
     author = {V. I. Buslaev},
     title = {Multipoint {Geronimus} and {Schur} parameters of measures on a~circle and on a~line},
     journal = {Sbornik. Mathematics},
     pages = {1007--1042},
     publisher = {mathdoc},
     volume = {215},
     number = {8},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2024_215_8_a0/}
}
TY  - JOUR
AU  - V. I. Buslaev
TI  - Multipoint Geronimus and Schur parameters of measures on a~circle and on a~line
JO  - Sbornik. Mathematics
PY  - 2024
SP  - 1007
EP  - 1042
VL  - 215
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2024_215_8_a0/
LA  - en
ID  - SM_2024_215_8_a0
ER  - 
%0 Journal Article
%A V. I. Buslaev
%T Multipoint Geronimus and Schur parameters of measures on a~circle and on a~line
%J Sbornik. Mathematics
%D 2024
%P 1007-1042
%V 215
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2024_215_8_a0/
%G en
%F SM_2024_215_8_a0
V. I. Buslaev. Multipoint Geronimus and Schur parameters of measures on a~circle and on a~line. Sbornik. Mathematics, Tome 215 (2024) no. 8, pp. 1007-1042. http://geodesic.mathdoc.fr/item/SM_2024_215_8_a0/