Overview
- Gives a brief, accessible, modern review of the history of the development of the mathematical theory of diffraction
- Covers techniques applicable to a wide range of problems
- Provides a detailed and well-illustrated explanation of an original method, missing in the present literature
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2249)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (21 chapters)
-
Front Matter
-
Method of Automorphic Functions on Complex Characteristics
-
Front Matter
-
Keywords
- Automorphic Functions
- Boundary Value Problem
- Complex Fourier Transform
- Diffraction
- Distributions
- Elliptic Equation
- Factorization
- Fredholm Operators
- Helmholtz Equation
- Holomorphic Functions
- Paley-Wiener Theorem
- Pseudo-differential Operators
- Riemann Surface
- Riemann-Hilbert Problem
- Wedge
- partial differential equations
About this book
This book presents a new and original method for the solution of boundary value problems in angles for second-order elliptic equations with constant coefficients and arbitrary boundary operators. This method turns out to be applicable to many different areas of mathematical physics, in particular to diffraction problems in angles and to the study of trapped modes on a sloping beach.
Giving the reader the opportunity to master the techniques of the modern theory of diffraction, the book introduces methods of distributions, complex Fourier transforms, pseudo-differential operators, Riemann surfaces, automorphic functions, and the Riemann–Hilbert problem.
The book will be useful for students, postgraduates and specialists interested in the application of modern mathematics to wave propagation and diffraction problems.
Authors and Affiliations
Bibliographic Information
Book Title: Stationary Diffraction by Wedges
Book Subtitle: Method of Automorphic Functions on Complex Characteristics
Authors: Alexander Komech, Anatoli Merzon
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-26699-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-26698-1Published: 17 September 2019
eBook ISBN: 978-3-030-26699-8Published: 16 September 2019
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XI, 167
Number of Illustrations: 16 b/w illustrations, 3 illustrations in colour
Topics: Mathematical Applications in the Physical Sciences, Mathematical Physics, Partial Differential Equations, Functions of a Complex Variable, Fourier Analysis