TY - JOUR
T1 - Norm preserving extensions of holomorphic functions defined on varieties in Cn
AU - Agler, Jim
AU - Kosiński, Łukasz
AU - McCarthy, John E.
N1 - Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/11/1
Y1 - 2022/11/1
N2 - If V is an analytic set in a pseudoconvex domain Ω, we show there is always a pseudoconvex domain G⊆Ω that contains V and has the property that every bounded holomorphic function on V extends to a bounded holomorphic function on G with the same norm. We find such a G for some particular analytic sets. When Ω is an operhedron we show there is a norm on holomorphic functions on V that can always be preserved by extensions to Ω.
AB - If V is an analytic set in a pseudoconvex domain Ω, we show there is always a pseudoconvex domain G⊆Ω that contains V and has the property that every bounded holomorphic function on V extends to a bounded holomorphic function on G with the same norm. We find such a G for some particular analytic sets. When Ω is an operhedron we show there is a norm on holomorphic functions on V that can always be preserved by extensions to Ω.
KW - Interpolation problem
KW - Noncommutative extensions
KW - Norm preserving extensions
UR - http://www.scopus.com/inward/record.url?scp=85136157316&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2022.109636
DO - 10.1016/j.jfa.2022.109636
M3 - Article
AN - SCOPUS:85136157316
SN - 0022-1236
VL - 283
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 9
M1 - 109636
ER -