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


Abstract


Let G : D ⊂ R<sup>n</sup> → R be a function. Any parametrized curve 𝛼 in D determines the composition g_𝛼 = G ○ 𝛼. If 𝛼 belongs to a family of curves, the family {g_𝛼} satisfies some conditions. Our goal is to find the conditions in which the families {𝛼}, g_𝛼 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.

DOI Code: 10.1285/i15900932v27n1p131

Keywords: Extension of maps; Function spaces; Γ-function; Generated functions

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