Preface ix -- 1. Introduction 1 -- 2. Distributions and Derivatives in the Sense of Distribution 7 -- 2.1 Functions and Distributions, 7 -- 2.2 Test Functions. The Space C∞ 0 , 9 -- 2.3 Convergence in D, 14 -- 2.4 Distribution, 16 -- 2.5 Some Simple Operations in D, 21 -- 2.5.1 Multiplication by a Real Number or a Function, 21 -- 2.5.2 Translation and Rescaling, 21 -- 2.5.3 Derivation of a Distribution, 22 -- 2.6 Order of a Distribution, 26 -- 2.7 The Support of a Distribution, 31 -- 2.8 Some Generalizations, 33 -- 2.8.1 Distributions on Multidimensional Spaces, 33 -- 2.8.2 Vector-Valued Distributions, 38 -- 3. Maxwell Equations in the Sense of Distribution 49 -- 3.1 Maxwell Equations Reduced into the Vacuum, 49 -- 3.1.1 Some Simple Examples, 53 -- 3.2 Universal Boundary Conditions and Compatibility Relations, 54 -- 3.2.1 An Example. Discontinuities on a Combined Sheet, 57 -- 3.3 The Concept of Material Sheet, 59 -- 3.4 The Case of Monochromatic Fields, 62 -- 3.4.1 Discontinuities on the Interface Between Two -- Simple Media that Are at Rest, 64 -- 4. Boundary Conditions on Material Sheets at Rest 67 -- 4.1 Universal Boundary Conditions and Compatibility Relations for a Fixed Material Sheet, 67 -- 4.2 Some General Results, 69 -- 4.3 Some Particular Cases, 70 -- 4.3.1 Planar Material Sheet Between Two Simple Media, 70 -- 4.3.2 Cylindrically or Spherically Curved Material Sheet Located Between Two Simple Media, 91 -- 4.3.3 Conical Material Sheet Located Between Two Simple Media, 93 -- 5. Discontinuities on a Moving Sheet 109 -- 5.1 Special Theory of Relativity, 110 -- 5.1.1 The Field Created by a Uniformly Moving Point Charge, 112 -- 5.1.2 The Expressions of the Field in a Reference System Attached to the Charged Particle, 114 -- 5.1.3 Lorentz Transformation Formulas, 115 -- 5.1.4 Transformation of the Electromagnetic Field, 118 -- 5.2 Discontinuities on a Uniformly Moving Surface, 120 -- 5.2.1 Transformation of the Universal Boundary Conditions, 123 -- 5.2.2 Transformation of the Compatibility Relations, 126.

5.2.3 Some Simple Examples, 126 -- 5.3 Discontinuities on a Nonuniformly Moving Sheet, 138 -- 5.3.1 Boundary Conditions on a Plane that Moves in a Direction Normal to Itself, 139 -- 5.3.2 Boundary Conditions on the Interface of Two Simple Media, 143 -- 6. Edge Singularities on Material Wedges Bounded by Plane Boundaries 149 -- 6.1 Introduction, 149 -- 6.2 Singularities at the Edges of Material Wedges, 153 -- 6.3 The Wedge with Penetrable Boundaries, 154 -- 6.3.1 The H Case, 156 -- 6.3.2 The E Case, 171 -- 6.4 The Wedge with Impenetrable Boundaries, 174 -- 6.5 Examples. Application to Half-Planes, 175 -- 6.6 Edge Conditions for the Induced Surface Currents, 176 -- 7. Tip Singularities at the Apex of a Material Cone 179 -- 7.1 Introduction, 179 -- 7.2 Algebraic Singularities of an H-Type Field, 185 -- 7.2.1 Contribution of the Energy Restriction, 185 -- 7.2.2 Contribution of the Boundary Conditions, 186 -- 7.3 Algebraic Singularities of an E-Type Field, 191 -- 7.4 The Case of Impenetrable Cones, 193 -- 7.5 Confluence and Logarithmic Singularities, 195 -- 7.6 Application to some Widely used Actual Boundary Conditions, 197 -- 7.7 Numerical Solutions of the Transcendental Equations Satisfied by the Minimal Index, 200 -- 7.7.1 The Case of Very Sharp Tip, 200 -- 7.7.2 The Case of Real-Valued Minimal v, 201 -- 7.7.3 A Function-Theoretic Method to Determine Numerically the Minimal v, 203 -- 8. Temporal Discontinuities 209 -- 8.1 Universal Initial Conditions, 209 -- 8.2 Linear Mediums in the Generalized Sense, 211 -- 8.3 An Illustrative Example, 212 -- References 215 -- Index 219 -- IEEE Press Series on Electromagnetic Wave Theory.