Author | Ramm, A. G. author |
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Title | Theory and Applications of Some New Classes of Integral Equations [electronic resource] / by A. G. Ramm |
Imprint | New York, NY : Springer New York, 1980 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-8112-9 |
Descript | XIV, 344 p. online resource |
I. 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 Greenโs 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 Greenโs Function -- Appendix 8. A Uniqueness Theorem for Schrรถdinger 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