Volterra Adventures

Volterra Adventures

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Description

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.
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Product details

  • Paperback | 248 pages
  • 140 x 216 x 19.05mm | 290.3g
  • Providence, United States
  • English
  • 1470441160
  • 9781470441166
  • 2,757,227

Table of contents

From Volterra to Banach: Starting out
Springing ahead
Springing higher
Operators as points
Travels with Titchmarsh: The Titchmarsh convolution theorem
Titchmarsh finale
Invariance through duality: Invariant subspaces
Digging into duality
Rendezvous with Riez
V-invariance: Finale
Uniform convergence
$\mathbb{C}$omplex primer
Uniform approximation by polynomials
Riemann-Stieltjes primer
Bibliography
Index
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About Joel H. Shapiro

Joel H. Shapiro, Portland State University, OR.
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