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Maxwell equation : inverse scattering in electromagnetism /

Hiroshi Isozaki, University of Tsukuba, Japan.

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Author: Isozaki, Hiroshi
Vernacular: Machine generated contents note: 1. Vector calculus -- 1.1. Implicit function theorem -- 1.2. Local definition of surfaces -- 1.3. Tangent space -- 1.4. Induced metric -- 1.5. Volume element -- 1.6. Global definition of surfaces -- 1.6.1. Submanifold of RN -- 1.6.2. Tangent space -- 1.6.3. Partition of unity -- 1.6.4. Integral on M -- 1.6.5. Convergence of volume integral to line integral -- 1.7. Integral formulas -- 1.7.1. Integration by parts -- 1.7.2. Theorem of Gauss-Ostrogradsky -- 1.7.3. Theorem of Green -- 1.7.4. Surfaces with boundaries -- 1.7.5. Stokes' Theorem -- 1.7.6. Integral of 1-form -- 1.8. A short course on differential forms -- 1.8.1. The case of two variables -- 1.8.2. The case of three variables -- 2. Fundamental solutions -- 2.1. Fundamental solution on Rn -- 2.2. Harmonic functions -- 2.3. Uniqueness theorem -- 2.4. Wave equation in Rn -- 2.4.1. d'Alembert's formula -- 2.4.2. Kirchhoff's formula -- 2.4.3. Poisson's formula -- 2.4.4. Huygens' principle -- 2.4.5. Duhamel's principle -- 2.4.6. Energy inequality -- 3. Potential theory -- 3.1. Dirac measure and principal value -- 3.2. Function spaces on S -- 3.3. Continuity of tangential derivatives -- 3.4. Single and double layer potentials -- 3.5. Dual space of a Banach space -- 3.6. Mapping properties -- 3.7. Fredholm's alternative theorem -- 3.7.1. Theory of Riesz-Schauder -- 3.7.2. Dual system -- 3.8. Boundary value problems for the Laplace equation -- 3.8.1. Boundary components -- 3.8.2. Uniqueness -- 3.8.3. Boundary integral equations on a single boundary -- 3.8.4. Boundary integral equations on multiple boundaries -- 3.9. Potential theory for the Helmholtz equation -- 3.9.1. Radiation condition -- 3.9.2. Uniqueness -- 3.9.3. Boundary integral equations -- 4. Maxwell equation -- 4.1. Equations in the vacuum -- 4.2. Gauge transformation -- 4.2.1. Existence of the potential -- 4.2.2. Coulomb gauge -- 4.2.3. Lorentz gauge -- 4.3. Biot-Savart's law -- 4.4. Linking number -- 4.5. Maxwell equation in medium -- 4.6. Conductor -- 4.6.1. Electrostatic capacity -- 4.6.2. Electrostatic shield -- 5. Cohomology -- 5.1. Bounded planar domain -- 5.2. Closed 2-dimensional surface -- 5.3. Handle body -- 5.4. Divergence free fields -- 5.5. Harmonic fields -- 5.6. Gradient fields -- 5.7. Hodge decomposition theorem -- 6. Initial value problem for the Maxwell equation -- 6.1. Fourier transform -- 6.1.1. Rapidly decreasing functions -- 6.1.2. Fourier transforms of L2-functions -- 6.1.3. Tempered distributions -- 6.2. Distributions with support on surfaces -- 6.3. Sobolev spaces -- 6.4. Fourier transformation and the Maxwell equation -- 6.5. Hilbert space approach -- 6.5.1. Self-adjoint operator and unitary group -- 6.5.2. Maxwell equation in the vacuum -- 6.5.3. Maxwell equation in the medium -- 7. Boundary value problem for the Maxwell equation -- 7.1. Curl and divergence spaces -- 7.1.1. Trace operator -- 7.1.2. Spaces H(div; Ω) and H(curl; Ω)) -- 7.2. Local compactness -- 7.3. Self-adjointness -- 7.4. Spectral properties of self-adjoint operators -- 7.4.1. Spectral measure -- 7.4.2. Classification of the spectrum -- 7.4.3. Local decay of scattering solutions -- 7.5. Spectrum of the Maxwell operator -- 7.5.1. Interior problem -- 7.5.2. Free Maxwell operator -- 7.5.3. Exterior problem -- 7.6. Time-dependent scattering theory -- 7.7. Tools from scattering theory -- 7.7.1. Functional calculus -- 7.7.2. Pseudo-differential calculus -- 8. Stationary scattering theory -- 8.1. Resolvent estimates for the free Laplacian -- 8.2. Resolvent estimates for the free Maxwell operator -- 8.3. Radiation condition -- 8.4. Resolvent estimates in an exterior domain -- 8.5. Spectral representation -- 8.6. The surjectivity of F± -- 8.7. S-matrix -- 8.8. Homogeneous equation -- 9. Scattering and interior boundary value problem -- 9.1. Mapping properties of the resolvent -- 9.2. Layer potentials -- 9.3. Mapping properties on Sobolev spaces -- 9.3.1. Function spaces -- 9.3.2. Layer potentials on Sobolev spaces -- 9.3.3. Perturbed layer potentials -- 9.4. E-M map -- 9.5. S-matrix determines E-M map -- 10. Inverse scattering -- 10.1. Green operators and scattering amplitudes -- 10.1.1. Abstract theory -- 10.1.2. Faddeev's Green operator -- 10.1.3. Green operator of Eskin-Raston -- 10.1.4. Inverse boundary value problem -- 10.2. Direction dependent Green operators for the free Maxwell equation -- 10.3. Perturbed direction dependent Green operators -- 10.4. From physical scattering amplitude to Faddeev scattering amplitude -- 10.5. Determination of medium -- 10.6. Anisotropic medium -- 10.7. Identifiability of the domain -- 10.8. Linear sampling method -- 10.9. Transmission eigenvalue -- 10.10. Determination of Betti number.
Published: Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd, [2018]
Topics: Maxwell equations. | Electromagnetic theory. | Electromagnetic theory. | Maxwell equations.
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Location & Availability for: Maxwell equation : inverse scattering in