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Singular Integral Equations

  • Ricardo Estrada
  • Ram P. Kanwal

Table of contents

  1. Front Matter
    Pages i-xii
  2. Ricardo Estrada, Ram P. Kanwal
    Pages 1-41
  3. Ricardo Estrada, Ram P. Kanwal
    Pages 43-69
  4. Ricardo Estrada, Ram P. Kanwal
    Pages 71-123
  5. Ricardo Estrada, Ram P. Kanwal
    Pages 125-174
  6. Ricardo Estrada, Ram P. Kanwal
    Pages 175-249
  7. Ricardo Estrada, Ram P. Kanwal
    Pages 251-293
  8. Ricardo Estrada, Ram P. Kanwal
    Pages 295-337
  9. Ricardo Estrada, Ram P. Kanwal
    Pages 339-374
  10. Ricardo Estrada, Ram P. Kanwal
    Pages 375-412
  11. Back Matter
    Pages 413-427

About this book

Introduction

Many physical problems that are usually solved by differential equation techniques can be solved more effectively by integral equation methods. This work focuses exclusively on singular integral equations and on the distributional solutions of these equations. A large number of beautiful mathematical concepts are required to find such solutions, which in tum, can be applied to a wide variety of scientific fields - potential theory, me­ chanics, fluid dynamics, scattering of acoustic, electromagnetic and earth­ quake waves, statistics, and population dynamics, to cite just several. An integral equation is said to be singular if the kernel is singular within the range of integration, or if one or both limits of integration are infinite. The singular integral equations that we have studied extensively in this book are of the following type. In these equations f (x) is a given function and g(y) is the unknown function. 1. The Abel equation x x) = l g (y) d 0 < a < 1. ( / Ct y, ( ) a X - Y 2. The Cauchy type integral equation b g (y) g(x)=/(x)+).. l--dy, a y-x where).. is a parameter. x Preface 3. The extension b g (y) a (x) g (x) = J (x) +).. l--dy , a y-x of the Cauchy equation. This is called the Carle man equation.

Keywords

Integral equations Potential differential equation distribution theory ksa potential theory statistics

Authors and affiliations

  • Ricardo Estrada
    • 1
  • Ram P. Kanwal
    • 2
  1. 1.Escuela de MatemáticaUniversidad de Costa RicaSan JoséCosta Rica
  2. 2.Department of MathematicsPenn State UniversityUniversity ParkUSA

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