ultraholomorphic
adjEtymology From ultra- + holomorphic.
1
Mathematics, Sciences Holomorphic and such that all derivatives are uniformly bounded by a constant multiple of the argument that can be associated with the order of the derivative.
- Under this assumption, and through the characterization of strongly regular sequences in terms of so-called regular variation, we show that the growth index #92;gamma(#92;mathbb#123;M#125;) defined by V.Thilliez (Division by flat ultradifferentiable functions and sectorial extensions, Results Math. 44 (2003), 169--188) and the order of quasianalyticity #92;omega(#92;mathbb#123;M#125;) introduced by the second author (Flat functions in Carleman ultraholomorphic classes via proximate orders, J.2015, Javier Jiménez-Garrido, Javier Sanz, “Strongly regular sequences and proximate orders”, in arXiv: