Curves in Banach spaces which allow a  C  2 ‐parameterization | Zendy

Duda Jakub | Zendy; Zajíček Luděk | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Curves in Banach spaces which allow a C 2 ‐parameterization

Author(s) -

Duda Jakub,

Zajíček Luděk

Publication year - 2011

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/jdq100

Subject(s) - banach space , characterization (materials science) , mathematics , bounded function , parametrization (atmospheric modeling) , norm (philosophy) , pure mathematics , derivative (finance) , space (punctuation) , mathematical analysis , discrete mathematics , physics , computer science , quantum mechanics , political science , law , optics , economics , radiative transfer , operating system , financial economics

We give a complete characterization of those f : [0, 1] → X (where X is a Banach space that has a Fréchet smooth norm) that allow an equivalent C 2 ‐parameterization. For X = ℝ, a characterization is well known. However, even in the case X = ℝ 2 , several quite new ideas are needed. Moreover, the very close case of parameterizations with a bounded second derivative is solved.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research