Courses :: Module, FUNCTIONAL ANALYSIS

	Overview
	Measure and Integration. Preliminary concepts. Positive Borel measures: Riesz Representation Theorem, Regularity properties. Lp spaces, completeness. Banach Spaces, continuous linear transformations, Hahn-Banach theorem, Open Mapping Theorem, Closed Graph Theorem, Uniform Boundedness Principle. Introduction to Hilbert Spaces. This module may be taught as a reading course.

Overview

Measure and Integration. Preliminary concepts. Positive Borel measures: Riesz Representation Theorem, Regularity properties. Lp spaces, completeness. Banach Spaces, continuous linear transformations, Hahn-Banach theorem, Open Mapping Theorem, Closed Graph Theorem, Uniform Boundedness Principle. Introduction to Hilbert Spaces.

This module may be taught as a reading course.

	Learning Outcomes
	On successful completion of the module, students should be able to: State some of the classical theorems of functional analysis. Prove any of the theorems given in the course. Deduce properties which follow from these theorems. Prove other analytic results using rigorous arguments.

Learning Outcomes

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? No No autumn repeat.

Autumn Supplementals/Resits

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FUNCTIONAL ANALYSIS

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