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Comparison of Clark Measures in Several Complex Variables. / Aleksandrov, Aleksei B.; Doubtsov, Evgueni.
Trends in Mathematics. Springer Nature, 2021. стр. 9-16 (Trends in Mathematics; Том 12).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › научная › Рецензирование
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TY - CHAP
T1 - Comparison of Clark Measures in Several Complex Variables
AU - Aleksandrov, Aleksei B.
AU - Doubtsov, Evgueni
N1 - Publisher Copyright: © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - Let D denote the unit disc of C and let Ω denote the unit ball Bn of Cn or the unit polydisc Dn, n≥ 2. Given a non-constant holomorphic function b: Ω → D, we study the corresponding family σα[ b], α∈ ∂D, of Clark measures on ∂Ω. For Ω = Bn and an inner function I: Bn→ D, we show that the property σ1[ I] ≪ σ1[ b] is directly related to the membership of an appropriate function in the de Branges–Rovnyak space H(b).
AB - Let D denote the unit disc of C and let Ω denote the unit ball Bn of Cn or the unit polydisc Dn, n≥ 2. Given a non-constant holomorphic function b: Ω → D, we study the corresponding family σα[ b], α∈ ∂D, of Clark measures on ∂Ω. For Ω = Bn and an inner function I: Bn→ D, we show that the property σ1[ I] ≪ σ1[ b] is directly related to the membership of an appropriate function in the de Branges–Rovnyak space H(b).
UR - http://www.scopus.com/inward/record.url?scp=85118549057&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-74417-5_2
DO - 10.1007/978-3-030-74417-5_2
M3 - Chapter
AN - SCOPUS:85118549057
T3 - Trends in Mathematics
SP - 9
EP - 16
BT - Trends in Mathematics
PB - Springer Nature
ER -
ID: 93204661