Eigenvalues, Embeddings and Generalised Trigonometric Functions

  • Jan Lang
  • David Edmunds

Part of the Lecture Notes in Mathematics book series (LNM, volume 2016)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Jan Lang, David Edmunds
    Pages 1-31
  3. Jan Lang, David Edmunds
    Pages 33-48
  4. Jan Lang, David Edmunds
    Pages 49-63
  5. Jan Lang, David Edmunds
    Pages 65-71
  6. Jan Lang, David Edmunds
    Pages 73-104
  7. Jan Lang, David Edmunds
    Pages 105-128
  8. Jan Lang, David Edmunds
    Pages 129-151
  9. Jan Lang, David Edmunds
    Pages 153-182
  10. Jan Lang, David Edmunds
    Pages 183-209
  11. Back Matter
    Pages 211-220

About this book

Introduction

The main theme of the book is the study, from the standpoint of s-numbers, of integral operators of Hardy type and related Sobolev embeddings. In the theory of s-numbers the idea is to attach to every bounded linear map between Banach spaces a monotone decreasing sequence of non-negative numbers with a view to the classification of operators according to the way in which these numbers approach a limit: approximation numbers provide an especially important example of such numbers. The asymptotic behavior of the s-numbers of Hardy operators acting between Lebesgue spaces is determined here in a wide variety of cases. The proof methods involve the geometry of Banach spaces and generalized trigonometric functions; there are connections with the theory of the p-Laplacian.

Keywords

41A35, 41A46, 47B06, 33E30, 47G10, 35P05 eigenvalues and eigenfunctions generalized trigonometric functions p-Laplacian s-numbers spectral theory on Banach spaces

Authors and affiliations

  • Jan Lang
    • 1
  • David Edmunds
    • 2
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA
  2. 2.Department of MathematicsUniversity of SussexBrightonUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-18429-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-18267-9
  • Online ISBN 978-3-642-18429-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
Industry Sectors
Electronics
Aerospace
Oil, Gas & Geosciences
Pharma