Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
1st Edition
Published on 26. February 2012
440 pages
978-1-4008-4269-8 (ISBN)
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Joram Lindenstrauss | David Preiss | Jaroslav Tiser
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
Book
02/2012
Princeton University Press
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Joram Lindenstrauss | David Preiss | Jaroslav Tiser
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
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02/2012
Princeton University Press
€254.50
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Persons
Joram Lindenstrauss is professor emeritus of mathematics at the Hebrew University of Jerusalem. David Preiss is professor of mathematics at the University of Warwick. Jaroslav Ti¿er is associate professor of mathematics at Czech Technical University in Prague.
Content
FrontMatter, pg. i
Contents, pg. vii
Chapter One: Introduction, pg. 1
Chapter Two: Gâteaux differentiability of Lipschitz functions, pg. 12
Chapter Three: Smoothness, convexity, porosity, and separable determination, pg. 23
Chapter Four: e-Fréchet differentiability, pg. 46
Chapter Five: G-null and Gn-null sets, pg. 72
Chapter Six: Férchet differentiability except for G-null sets, pg. 96
Chapter Seven: Variational principles, pg. 120
Chapter Eight: Smoothness and asymptotic smoothness, pg. 133
Chapter Nine: Preliminaries to main results, pg. 156
Chapter Ten: Porosity, Gn- and G-null sets, pg. 169
Chapter Eleven: Porosity and e-Fréchet differentiability, pg. 202
Chapter Twelve: Fréchet differentiability of real-valued functions, pg. 222
Chapter Thirteen: Fréchet differentiability of vector-valued functions, pg. 262
Chapter Fourteen: Unavoidable porous sets and nondifferentiable maps, pg. 319
Chapter Fifteen: Asymptotic Fréchet differentiability, pg. 355
Chapter Sixteen: Differentiability of Lipschitz maps on Hilbert spaces, pg. 392
Bibliography, pg. 415
Index, pg. 419
Index of Notation, pg. 423
Contents, pg. vii
Chapter One: Introduction, pg. 1
Chapter Two: Gâteaux differentiability of Lipschitz functions, pg. 12
Chapter Three: Smoothness, convexity, porosity, and separable determination, pg. 23
Chapter Four: e-Fréchet differentiability, pg. 46
Chapter Five: G-null and Gn-null sets, pg. 72
Chapter Six: Férchet differentiability except for G-null sets, pg. 96
Chapter Seven: Variational principles, pg. 120
Chapter Eight: Smoothness and asymptotic smoothness, pg. 133
Chapter Nine: Preliminaries to main results, pg. 156
Chapter Ten: Porosity, Gn- and G-null sets, pg. 169
Chapter Eleven: Porosity and e-Fréchet differentiability, pg. 202
Chapter Twelve: Fréchet differentiability of real-valued functions, pg. 222
Chapter Thirteen: Fréchet differentiability of vector-valued functions, pg. 262
Chapter Fourteen: Unavoidable porous sets and nondifferentiable maps, pg. 319
Chapter Fifteen: Asymptotic Fréchet differentiability, pg. 355
Chapter Sixteen: Differentiability of Lipschitz maps on Hilbert spaces, pg. 392
Bibliography, pg. 415
Index, pg. 419
Index of Notation, pg. 423
