Extension of functions in Rⁿ

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

[img] PDF (MS dissertation of Debanjan Nandi)
Debanjan_Nandi.pdf - Submitted Version
Restricted to Repository staff only

Download (515kB)
Official URL: http://www.iiserkol.ac.in


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 07:18
Last Modified: 19 Jan 2015 07:19
URI: http://eprints.iiserkol.ac.in/id/eprint/236

Actions (login required)

View Item View Item