Page 20 - Handbook Of Integral Equations

11.20. Regularization Method for Equations With Infinite Limits of Integration
11.20-1. Basic Equation and Fredholm Theorems
11.20-2. Regularizing Operators
11.20-3. The Regularization Method
12. Methods for Solving Singular Integral Equations of the First Kind
12.1. Some Definitions and Remarks
12.1-1. Integral Equations of the First Kind With Cauchy Kernel
12.1-2. Integral Equations of the First Kind With Hilbert Kernel
12.2. The Cauchy Type Integral
12.2-1. Definition of the Cauchy Type Integral
12.2-2. The H¨ older Condition
12.2-3. The Principal Value of a Singular Integral
12.2-4. Multivalued Functions
12.2-5. The Principal Value of a Singular Curvilinear Integral
12.2-6. The Poincar´ e–Bertrand Formula
12.3. The Riemann Boundary Value Problem
12.3-1. The Principle of Argument. The Generalized Liouville Theorem
12.3-2. The Hermite Interpolation Polynomial
12.3-3. Notion of the Index
12.3-4. Statement of the Riemann Problem
12.3-5. The Solution of the Homogeneous Problem
12.3-6. The Solution of the Nonhomogeneous Problem
12.3-7. The Riemann Problem With Rational Coefficients
12.3-8. The Riemann Problem for a Half-Plane
12.3-9. Exceptional Cases of the Riemann Problem
12.3-10. The Riemann Problem for a Multiply Connected Domain
12.3-11. The Cases of Discontinuous Coefficients and Nonclosed Contours
12.3-12. The Hilbert Boundary Value Problem
12.4. Singular Integral Equations of the First Kind
12.4-1. The Simplest Equation With Cauchy Kernel
12.4-2. An Equation With Cauchy Kernel on the Real Axis
12.4-3. An Equation of the First Kind on a Finite Interval
12.4-4. The General Equation of the First Kind With Cauchy Kernel
12.4-5. Equations of the First Kind With Hilbert Kernel
12.5. Multhopp–Kalandiya Method
12.5-1. A Solution That is Unbounded at the Endpoints of the Interval
12.5-2. A Solution Bounded at One Endpoint of the Interval
12.5-3. Solution Bounded at Both Endpoints of the Interval
13. Methods for Solving Complete Singular Integral Equations
13.1. Some Definitions and Remarks
13.1-1. Integral Equations With Cauchy Kernel
13.1-2. Integral Equations With Hilbert Kernel
13.1-3. Fredholm Equations of the Second Kind on a Contour
13.2. The Carleman Method for Characteristic Equations
13.2-1. A Characteristic Equation With Cauchy Kernel
13.2-2. The Transposed Equation of a Characteristic Equation
13.2-3. The Characteristic Equation on the Real Axis
13.2-4. The Exceptional Case of a Characteristic Equation

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
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