ultradifferentiable en · ADJ
Etymology
Etymology tree Proto-Indo-European *h₂el- Latin ūls Proto-Indo-European *-teros? Latin -ter Old Latin -ād Latin -ā Latin ultrābor. English ultra- Proto-Indo-European *dwóh₁ ▲ Proto-Indo-European *trísinflu. Proto-Indo-European *d(w)is- Proto-Italic *dis- Latin dis- Proto-Indo-European *bʰer- Proto-Indo-European *-eti Proto-Indo-European *bʰéreti Proto-Italic *ferō Latin ferō Latin differō Latin differēns Proto-Indo-European *-(i)yós Proto-Italic *-ijos Proto-Italic *-ios Old Latin -ios Latin -ius Latin -ia Latin differentia New Latin differentiō New Latin differentiātusbor. English differentiate Proto-Indo-European *-dʰlom Proto-Italic *-ðlom Proto-Italic *-ðlis Latin -bilis Latin -ābilis Old French -ablebor. Middle English -able English -able English differentiable English ultradifferentiable From ultra- + differentiable.
Meanings
-
(not-comparable) Having all derivatives over an open set bounded by an indexed value in an ultradistribution (times a constant).
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: