Результаты исследований: Научные публикации в периодических изданиях › статья
Localization of Zeros for Cauchy Transforms. / Abakumov, E.; Baranov, A.; Belov, Y.
в: International Mathematics Research Notices, Том 15, 2015, стр. 6699-6733.Результаты исследований: Научные публикации в периодических изданиях › статья
}
TY - JOUR
T1 - Localization of Zeros for Cauchy Transforms
AU - Abakumov, E.
AU - Baranov, A.
AU - Belov, Y.
PY - 2015
Y1 - 2015
N2 - We study the localization of zeros of Cauchy transforms of discrete measures on the real line. This question is motivated by the theory of canonical systems of differential equations. In particular, we prove that the spaces of Cauchy transforms having the localization property are in one-to-one correspondence with the canonical systems of special type, namely, those whose Hamiltonians consist only of indivisible intervals accumulating on the left. Various aspects of the localization phenomena are studied in details. Connections with the density of polynomials and other topics in analysis are discussed.
AB - We study the localization of zeros of Cauchy transforms of discrete measures on the real line. This question is motivated by the theory of canonical systems of differential equations. In particular, we prove that the spaces of Cauchy transforms having the localization property are in one-to-one correspondence with the canonical systems of special type, namely, those whose Hamiltonians consist only of indivisible intervals accumulating on the left. Various aspects of the localization phenomena are studied in details. Connections with the density of polynomials and other topics in analysis are discussed.
U2 - 10.1093/imrn/rnu142
DO - 10.1093/imrn/rnu142
M3 - Article
VL - 15
SP - 6699
EP - 6733
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
ER -
ID: 3988567