Integral Equations of First Kind

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World Scientific, 1995 - Mathematics - 265 pages
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This book studies classes of linear integral equations of the first kind most often met in applications. Since the general theory of integral equations of the first kind has not been formed yet, the book considers the equations whose solutions either are estimated in quadratures or can be reduced to well-investigated classes of integral equations of the second kind.In this book the theory of integral equations of the first kind is constructed by using the methods of the theory of functions both of real and complex variables. Special attention is paid to the inversion formulas of model equations most often met in physics, mechanics, astrophysics, chemical physics etc. The general theory of linear equations including the Fredholm, the Noether, the Hausdorff theorems, the Hilbert-Schmidt theorem, the Picard theorem and the application of this theory to the solution of boundary problems are given in this book. The book studies the equations of the first kind with the Schwarz Kernel, the Poisson and the Neumann kernels; the Volterra integral equations of the first kind, the Abel equations and some generalizations, one-dimensional and many-dimensional analogues of the Cauchy type integral and some of their applications.
 

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Contents

General Remarks on Linear Integral Equations of
27
The Picard Theorem of Solvability of a Class of Integral
51
Integral Equations of the First Kind with Kernels
81
Integral Equations of the First Kind with the Kernels
103
Some Other Classes of Integral Equation of the First Kind
125
The Abel Integral Equation and Some of Its Generalizations
181
A TwoDimensional Analogue of the Cauchy Type Integral
215
References
259
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