**Student Mathematical Library**

Volume: 85;
2018;
219 pp;
Softcover

MSC: Primary 46; 45;

Print ISBN: 978-1-4704-4116-6

Product Code: STML/85

List Price: $52.00

Individual Price: $41.60

**Electronic ISBN: 978-1-4704-4733-5
Product Code: STML/85.E**

List Price: $52.00

Individual Price: $41.60

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#### Supplemental Materials

# Volterra Adventures

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*Joel H. Shapiro*

This book introduces functional analysis to undergraduate mathematics students who possess a basic background in analysis and linear algebra. By studying how the Volterra operator acts on vector spaces of continuous functions, its readers will sharpen their skills, reinterpret what they already know, and learn fundamental Banach-space techniques—all in the pursuit of two celebrated results: the Titchmarsh Convolution Theorem and the Volterra Invariant Subspace Theorem. Exercises throughout the text enhance the material and facilitate interactive study.

#### Readership

Undergraduate students interested in functional analysis and operator theory.

#### Reviews & Endorsements

I would recommend this book to anyone seeking a pleasant read on functional analysis. The book elegantly and clearly traverses the varied paths of mathematics (algebraic and analytical, real and complex, finite and transfinite), gently leading the reader to profound and relevant results of modern analysis.

-- Daniel M. Pellegrino, Mathematical Reviews

The author has worked hard to make these topics accessible to undergraduates who have taken (good) courses in linear algebra and real analysis...The exposition is, throughout the book, of very high quality. Shapiro is a talented writer, and he knows how to explain things clearly and engagingly, in easily-digested pieces for an undergraduate audience...it will offer students an accessible, stimulating, and informative look at a beautiful branch of mathematics.

-- Mark Hunacek, MAA Reviews

#### Table of Contents

# Table of Contents

## Volterra Adventures

- Cover 11
- Title page 44
- Contents 88
- Preface 1212
- List of Symbols 1616
- Part 1 . From Volterra to Banach 1818
- Part 2 . Travels with Titchmarsh 9696
- Part 3 . Invariance Through Duality 130130
- Chapter 7. Invariant Subspaces 132132
- Chapter 8. Digging into Duality 150150
- Chapter 9. Rendezvous with Riesz 172172
- Chapter 10. V-Invariance: Finale 190190
- Appendix A. Uniform Convergence 200200
- Appendix B. \CComplex Primer 202202
- Appendix C. Uniform Approximation by Polynomials 212212
- Appendix D. Riemann-Stieltjes Primer 216216
- Bibliography 230230
- Index 234234

- Back Cover 240240