TY - JOUR
T1 - Semigroups of holomorphic functions and condenser capacity
AU - Betsakos, Dimitrios
AU - Kelgiannis, Georgios
AU - Kourou, Maria
AU - Pouliasis, Stamatis
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - Suppose (ϕt)t≥0 is a semigroup of holomorphic functions in the unit disk D with Denjoy–Wolff point τ= 1. Suppose K is a compact subset of D. We prove that the capacity of the condenser (D, ϕt(K)) is a decreasing function of t. Moreover, we study its asymptotic behavior as t→ + ∞ in relation with the type of the semigroup.
AB - Suppose (ϕt)t≥0 is a semigroup of holomorphic functions in the unit disk D with Denjoy–Wolff point τ= 1. Suppose K is a compact subset of D. We prove that the capacity of the condenser (D, ϕt(K)) is a decreasing function of t. Moreover, we study its asymptotic behavior as t→ + ∞ in relation with the type of the semigroup.
KW - Condenser capacity
KW - Green capacity
KW - Hyperbolic semigroup
KW - Koenigs function
KW - Parabolic semigroup
KW - Semigroup of holomorphic functions
UR - http://www.scopus.com/inward/record.url?scp=85077308587&partnerID=8YFLogxK
U2 - 10.1007/s13324-019-00344-4
DO - 10.1007/s13324-019-00344-4
M3 - Article
AN - SCOPUS:85077308587
SN - 1664-2368
VL - 10
JO - Analysis and Mathematical Physics
JF - Analysis and Mathematical Physics
IS - 1
M1 - 8
ER -