Extension of functions in Rⁿ

Nandi, Debanjan (2014) Extension of functions in Rⁿ. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

In this thesis we study some problems on the possibility of the existence of an extension satisfying certain conditions of a real-valued function depned on a subset E of Rⁿ. Namely, we study the necessary and suficient conditions for a function f : E → R to admit an extension F : Rⁿ → R that satisfies at least one of the following three conditions : (a) C⁰(Rⁿ)-F is continuous (b) C⁰̓¹(Rⁿ)-F is Lipschitz (c) Cᵐ(Rⁿ)-F has continuous partial derivatives of all orders less than or equal to m.

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