Construction of a function using its values along $C<sup>1</sup>$ curves

Authors

  • Oltin Dogaru

DOI:

https://doi.org/10.1285/i15900932v27n1p131

Keywords:

Extension of maps, Function spaces, Γ-function, Generated functions

Abstract

Let $G : D ⊂ Rn → R$ be a function. Any parametrized curve ? in D determines the composition $g_? = G ○ ?$. If ? belongs to a family of curves, the family ${g_?}$ satisfies some conditions. Our goal is to find the conditions in which the families {?}, $g_?$ determine the function G. Section 1 emphasizes the origin of the problem. Section 2 defines and studies the notion of the Γ function. Section 3 presents the construction of a function using a Γ-function.

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Published

04-08-2009

Issue

Volume 27, Issue 1 (2007)

Section

Articoli

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http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode