Studies in the History of Mathematics and Physical Sciences

The Prehistory of the Theory of Distributions

Authors: Lützen, J.

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About this book

I first learned the theory of distributions from Professor Ebbe Thue Poulsen in an undergraduate course at Aarhus University. Both his lectures and the textbook, Topological Vector Spaces, Distributions and Kernels by F. Treves, used in the course, opened my eyes to the beauty and abstract simplicity of the theory. However my incomplete study of many branches of classical analysis left me with the question: Why is the theory of distributions important? In my continued studies this question was gradually answered, but my growing interest in the history of mathematics caused me to alter my question to other questions such as: For what purpose, if any, was the theory of distributions originally created? Who invented distributions and when? I quickly found answers to the last two questions: distributions were invented by S. Sobolev and L. Schwartz around 1936 and 1950, respectively. Knowing this answer, however, only created a new question: Did Sobolev and Schwartz construct distributions from scratch or were there earlier trends and, if so, what were they? It is this question, concerning the pre­ history of the theory of distributions, which I attempt to answer in this book. Most of my research took place at the History of Science Department of Aarhus University. I wish to thank this department for its financial and intellectual support. I am especially grateful to Lektors Kirsti Andersen from the History of Science Department and Lars Mejlbo from the Mathematics Department, for their kindness, constructive criticism, and encouragement.

Table of contents (8 chapters)

  • Introduction

    Lützen, Jesper

    Pages 1-5

  • Distributions in the Development of Functional Analysis

    Lützen, Jesper

    Pages 6-12

  • Generalized Differentiation and Generalized Solutions to Differential Equations

    Lützen, Jesper

    Pages 13-72

  • Generalized Fourier Transforms

    Lützen, Jesper

    Pages 73-91

  • Early Generalized Functions

    Lützen, Jesper

    Pages 92-143

Buy this book

eBook $74.99
price for USA (gross)
  • ISBN 978-1-4613-9472-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-1-4613-9474-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Prehistory of the Theory of Distributions
Authors
Series Title
Studies in the History of Mathematics and Physical Sciences
Series Volume
7
Copyright
1982
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4613-9472-3
DOI
10.1007/978-1-4613-9472-3
Softcover ISBN
978-1-4613-9474-7
Series ISSN
0172-570X
Edition Number
1
Number of Pages
232
Topics