ABSTRACT

Equations of Mathematical Diffraction Theory focuses on the comparative analysis and development of efficient analytical methods for solving equations of mathematical diffraction theory. Following an overview of some general properties of integral and differential operators in the context of the linear theory of diffraction processes, the authors provide estimates of the operator norms for various ranges of the wave number variation, and then examine the spectral properties of these operators. They also present a new analytical method for constructing asymptotic solutions of boundary integral equations in mathematical diffraction theory for the high-frequency case.

Clearly demonstrating the close connection between heuristic and rigorous methods in mathematical diffraction theory, this valuable book provides you with the differential and integral equations that can easily be used in practical applications.

chapter 1|5 pages

Some Preliminaries from Analysis and the Theory of Wave Processes

Integrands, and Series in Residues

chapter |8 pages

Helpful remarks

chapter |1 pages

Helpful remarks

chapter |4 pages

mCylyA | y -y| OyBl

chapter 3|3 pages

Wave Fields in a Layer of Constant Thickness

Homogeneous and Inhomogeneous Waves

chapter |15 pages

Helpful remarks

chapter |2 pages

y1-4bxa

chapter |1 pages

y 7-12 c1-6x

chapter |10 pages

y 13-24 c 1-12 x

chapter |23 pages

Helpful remarks

chapter 6|4 pages

Short-Wave Asymptotic Methods on the Basis of Multiple Integrals

Fields by One-Dimensional Quadratures

chapter |1 pages

Helpful remarks

chapter |1 pages

ak /p

chapter |4 pages

xxnLLyy

chapter |6 pages

Helpful remarks

chapter |2 pages

|A| 8q6420 90 180 270 q, degrees

chapter |5 pages

xnqnSqnS

chapter 8|22 pages

Ill-Posed Equations of Inverse Diffraction Problems for Arbitrary Boundary

First Kind: General Properties

chapter |1 pages

xbaOxxOx

chapter x|5 pages

1 -1 1xO -1

chapter |9 pages

g(y) -5 -4 -3 -2 0 120 ° 240 °

chapter |3 pages

xxxx

chapter 9|9 pages

Numerical Methods for Irregular Operator Equations

Improvement of the Convergence