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Differential Analysis in Infinite Dimensional Spaces
Edited by: Kondagunta Sundaresan and Srinivasa Swaminathan
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Contemporary Mathematics
1986; 122 pp; softcover
Volume: 54
ISBN-10: 0-8218-5059-8
ISBN-13: 978-0-8218-5059-6
List Price: US$29
Member Price: US$23.20
Order Code: CONM/54
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This volume focuses on developments made in the past two decades in the field of differential analysis in infinite dimensional spaces. New techniques such as ultraproducts and ultrapowers have illuminated the relationship between the geometric properties of Banach spaces and the existence of differentiable functions on the spaces. The wide range of topics covered also includes gauge theories, polar subsets, approximation theory, group analysis of partial differential equations, inequalities, and actions on infinite groups.

Addressed to both the expert and the advanced graduate student, the book requires a basic knowledge of functional analysis and differential topology.

Table of Contents

  • M. S. Berger -- The impact of gauge theories on nonlinear infinite dimensional analysis
  • S. Dineen -- Polar subsets in infinite dimensional spaces-small sets in large spaces
  • M. P. Heble -- Approximation of differentiable functions on a Hilbert space, II
  • C. C. A. Sastri -- Group analysis of some partial differential equations arising in applications
  • M.-H. Shih and K.-K. Tan -- Minimax inequalities and applications
  • T. N. Subramanian -- Slices for actions of infinite dimensional groups
  • K. Sundaresan -- Convex functions on Banach lattices
  • K. Sundaresan and S. Swaminathan -- Differential analysis and geometry of Banach spaces-isomorphism theory
  • J. H. M. Whitfield and V. Zizler -- A survey of rough norms with applications
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