Ebook: Singular Integral Equations
- Tags: Analysis, Applications of Mathematics, Theoretical Mathematical and Computational Physics, Statistical Theory and Methods
- Year: 2000
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-xii
Reference Material....Pages 1-41
Abel’s and Related Integral Equations....Pages 43-69
Cauchy Type Integral Equations....Pages 71-123
Carleman Type Integral Equations....Pages 125-174
Distributional Solutions of Singular Integral Equations....Pages 175-249
Distributional Equations on the Whole Line....Pages 251-293
Integral Equations with Logarithmic Kernels....Pages 295-337
Wiener-Hopf Integral Equations....Pages 339-374
Dual and Triple Integral Equations....Pages 375-412
Back Matter....Pages 413-427
Content:
Front Matter....Pages i-xii
Reference Material....Pages 1-41
Abel’s and Related Integral Equations....Pages 43-69
Cauchy Type Integral Equations....Pages 71-123
Carleman Type Integral Equations....Pages 125-174
Distributional Solutions of Singular Integral Equations....Pages 175-249
Distributional Equations on the Whole Line....Pages 251-293
Integral Equations with Logarithmic Kernels....Pages 295-337
Wiener-Hopf Integral Equations....Pages 339-374
Dual and Triple Integral Equations....Pages 375-412
Back Matter....Pages 413-427
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