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# Theory and Applications of Some New Classes of Integral Equations by Alexander G. Ramm (Paperback, 1980)

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## About this product

### Key Features

- Author(s)Alexander G. Ramm
- PublisherSpringer-Verlag New York Inc.
- Date of Publication01/12/1980
- Language(s)English
- FormatPaperback
- ISBN-100387905405
- ISBN-139780387905402
- GenreMathematics

### Publication Data

- Place of PublicationNew York, NY
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Notebiography

### Dimensions

- Weight527 g
- Width152 mm
- Height229 mm
- Spine19 mm
- Pagination344

### Editorial Details

- Edition StatementSoftcover reprint of the original 1st ed. 1980

### Description

- Table Of ContentsI. Investigation of a New Class of Integral Equations and Applications to Estimation Problems (Filtering, Prediction, System Identification).- 1. Statement of the Problems and Main Results.- 2. Investigation of the Scalar Equations.- 3. Investigation of the Vector Equations.- 4. Investigation of the Multidimensional Equations.- 5. Approximate Solution of the Integral Equations in the Space of Distributions.- 6. Asymptotics of the Spectrum of the Investigated Integral Equations.- 7. General Theorems about Perturbations Preserving the Asymptotics of a Spectrum.- 8. Remarks and Examples.- 9. Research Problems.- 10. Bibliographical Note.- II. Investigation of Integral Equations of the Static and Quasi-Static Fields and Applications to the Scattering from Small Bodies of Arbitrary Shape.- 0. Introduction.- 1. Statement of the Problems and Main Results.- 2. Investigation of a Class of Linear Operator Equations.- 3. Integral Equations of Static Field Theory for a Single Body and Their Applications. Explicit Formulas for the Scattering Matrix in the Problem of Wave Scattering from a Small Body of Arbitrary Shape.- 4. Variational Principles for Calculation of the Electrical Capacitance and Polarizability Tensors for Bodies of Arbitrary Shape and Two-Sided Estimates of the Tensors.- 5. Inverse Problem of Radiation Theory.- 6. Wave Scattering by a System of Small Bodies; Formulas for the Scattering Amplitude; and Determination of the Medium Properties from the Scattering Data.- 7. Research Problems.- 8. Bibliographical Note.- III. Investigation of a Class of Nonlinear Integral Equations and Applications to Nonlinear Network Theory.- 0. Introduction.- 1. Statement of the Problems and Main Results.- 2. Existence, Uniqueness and Stability of Solutions of Some Nonlinear Operator Equations and an Iterative Process to Solve the Equations.- 3. Existence, Uniqueness, and Stability of the Stationary Regimes in Some Nonlinear Networks. Stability in the Large and Convergence in the Nonlinear Networks.- 4. Stationary Regime in a Nonlinear Feedback Amplifier.- 5. Research Problems.- 6. Bibliographical Note.- IV. Integral Equations Arising in the Open System Theory.- 1. Calculation of the Complex Poles of Green's Function in Scattering and Diffraction Problems.- 2. Calculation of Diffraction Losses in Some Open Resonators.- 3. Some Spectral Properties of Nonselfadjoint Integral Operators of Diffraction Theory.- 4. Research Problems.- 5. Bibliographical Note.- V. Investigation of Some Integral Equations Arising in Antenna Synthesis.- 1. A Method for Stable Solution of an Equation of the First Kind.- 2. Some Results Concerning the General Antenna Synthesis Problem.- 3. Formula for Approximation by Entire Functions.- 4. Nonlinear Synthesis Problems.- 5. Inverse Diffraction Problems.- 6. Optimal Solution to the Antenna Synthesis Problem.- 7. Research Problems.- 8. Bibliographical Note.- Appendix 1. Stable Solution of the Integral Equation of the Inverse Problem of Potential Theory.- Appendix 2. Iterative Processes for Solving Boundary Value Problems.- Appendix 3. Electromagnetic Wave Scattering by Small Bodies.- Appendix 4. Two-Sided Estimates of the Scattering Amplitude for Low Energies.- Appendix 5. Variational Principles, for Eigenvalues of Compact Nonselfadjoint Operators.- Appendix 6. Boundary-Value Problems with Discontinuous Boundary Conditions.- Appendix 7. Poles of Green's Function.- Appendix 8. A Uniqueness Theorem for Schrodinger Equation.- Appendix 9. Stable Solution of Integral Equations of the First Kind with Logarithmic Kernels.- Appendix 10. Nonselfadjoint Operators in Diffraction and Scattering.- Appendix 11. On the Basis Property for the Root Vectors of Some Nonselfadjoint Operators.- Bibliographical Notes for Appendices.- List of Symbols.- Author Index.

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