Skip to main content
SpringerLink
Log in

Existence Families, Functional Calculi and Evolution Equations

  • Book
  • © 1994

Overview

Authors:
  1. Ralph deLaubenfels
    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1570)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (31 chapters)

  1. Front Matter

    Pages I-XV
    Download chapter PDF

  2. Intuition and elementary examples

    • Ralph deLaubenfels
    Pages 1-6

  3. Existence families

    • Ralph deLaubenfels
    Pages 7-12

  4. Regularized semigroups

    • Ralph deLaubenfels
    Pages 13-23

  5. The solution space of an operator and automatic well-posedness

    • Ralph deLaubenfels
    Pages 24-37

  6. Exponentially bounded (Banach) solution spaces

    • Ralph deLaubenfels
    Pages 38-54

  7. Well-posedness on a larger space; Generalized solutions

    • Ralph deLaubenfels
    Pages 55-59

  8. Entire vectors and entire existence families

    • Ralph deLaubenfels
    Pages 60-65

  9. Reversibility of parabolic problems

    • Ralph deLaubenfels
    Pages 66-70

  10. The cauchy problem for the Laplace equation

    • Ralph deLaubenfels
    Pages 71-72

  11. Boundary values of holomorphic semigroups

    • Ralph deLaubenfels
    Pages 73-75

  12. The Schrödinger equation

    • Ralph deLaubenfels
    Pages 76-78

  13. Functional calculus for commuting generators of bounded strongly continuous groups

    • Ralph deLaubenfels
    Pages 79-85

  14. Petrovsky correct matrices of generators of bounded strongly continuous groups

    • Ralph deLaubenfels
    Pages 86-91

  15. Arbitrary matrices of generators of bounded strongly continuous groups

    • Ralph deLaubenfels
    Pages 92-93

  16. More examples of regularized semigroups

    • Ralph deLaubenfels
    Pages 94-96

  17. Existence and uniqueness families

    • Ralph deLaubenfels
    Pages 97-103

  18. C-resolvents and Hille-Yosida type theorems

    • Ralph deLaubenfels
    Pages 104-109

  19. Relationship to integrated semigroups

    • Ralph deLaubenfels
    Pages 110-112

  20. Perturbations

    • Ralph deLaubenfels
    Pages 113-124
Back to top

Keywords

About this book

This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, organized way, together with a great deal of new material.

Bibliographic Information

  • Book Title: Existence Families, Functional Calculi and Evolution Equations

  • Authors: Ralph deLaubenfels

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0073401

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Softcover ISBN: 978-3-540-57703-4Published: 28 March 1994

  • eBook ISBN: 978-3-540-48322-9Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVI, 244

  • Topics: Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation