The Riesz Representation Theorem

PDF Version Also Available for Download.

Description

In 1909, F. Riesz succeeded in giving an integral represntation for continuous linear functionals on C[0,1]. Although other authors, notably Hadamard and Frechet, had given representations for continuous linear functionals on C[0,1], their results lacked the clarity, elegance, and some of the substance (uniqueness) of Riesz's theorem. Subsequently, the integral representation of continuous linear functionals has been known as the Riesz Representation Theorem. In this paper, three different proofs of the Riesz Representation Theorem are presented. The first approach uses the denseness of the Bernstein polynomials in C[0,1] along with results of Helly to write the continuous linear functionals as ... continued below

Physical Description

72 leaves

Creation Information

Williams, Stanley C. (Stanley Carl) August 1980.

Context

This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 168 times , with 11 in the last month . More information about this thesis can be viewed below.

Who

People and organizations associated with either the creation of this thesis or its content.

Chair

Committee Member

Publisher

Rights Holder

For guidance see Citations, Rights, Re-Use.

  • Williams, Stanley C. (Stanley Carl)

Provided By

UNT Libraries

The UNT Libraries serve the university and community by providing access to physical and online collections, fostering information literacy, supporting academic research, and much, much more.

Contact Us

What

Descriptive information to help identify this thesis. Follow the links below to find similar items on the Digital Library.

Degree Information

Description

In 1909, F. Riesz succeeded in giving an integral represntation for continuous linear functionals on C[0,1]. Although other authors, notably Hadamard and Frechet, had given representations for continuous linear functionals on C[0,1], their results lacked the clarity, elegance, and some of the substance (uniqueness) of Riesz's theorem. Subsequently, the integral representation of continuous linear functionals has been known as the Riesz Representation Theorem. In this paper, three different proofs of the Riesz Representation Theorem are presented. The first approach uses the denseness of the Bernstein polynomials in C[0,1] along with results of Helly to write the continuous linear functionals as Stieltjes integrals. The second approach makes use of the Hahn-Banach Theorem in order to write the functional as an integral. The paper concludes with a detailed presentation of a Daniell integral development of the Riesz Representation Theorem.

Physical Description

72 leaves

Subjects

Language

Identifier

Unique identifying numbers for this thesis in the Digital Library or other systems.

Collections

This thesis is part of the following collection of related materials.

UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

What responsibilities do I have when using this thesis?

When

Dates and time periods associated with this thesis.

Creation Date

  • August 1980

Added to The UNT Digital Library

  • May 10, 2015, 6:16 a.m.

Description Last Updated

  • Feb. 6, 2017, 9:43 a.m.

Usage Statistics

When was this thesis last used?

Yesterday: 0
Past 30 days: 11
Total Uses: 168

Interact With This Thesis

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Williams, Stanley C. (Stanley Carl). The Riesz Representation Theorem, thesis, August 1980; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc504232/: accessed September 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .