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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.

    Item Type: Thesis (Masters)
    Additional Information: Supervisor: Dr. Himadri Mukherjee
    Uncontrolled Keywords: Extension; Lipschitz; Mathematical Function; Rⁿ
    Subjects: Q Science > QA Mathematics
    Divisions: Department of Mathematics and Statistics
    Depositing User: IISER Kolkata Librarian
    Date Deposited: 19 Jan 2015 12:48
    Last Modified: 19 Jan 2015 12:49
    URI: http://eprints.iiserkol.ac.in/id/eprint/236

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