The Three-Dimensional Inverse Scattering Problem (Classic Reprint) - Hardcover

Irvin W. Kay

Hardcover

ISBN 10: 036456301X ISBN 13: 9780364563014

Publisher: Forgotten Books, 2018

Synopsis

Explore how to uncover hidden structures from scattered waves. This book guides you through a rigorous approach to determine material properties from measured scattering data.

The work analyzes the problem of finding how electron density varies in a weakly ionized gas by using the scattering amplitude from a plane electromagnetic wave. It develops a framework that treats wave propagation with a scalar model and connects the inverse problem to integral equations, spectral weights, and scattering operators. Readers will see how different mathematical tools come together to address a physically motivated, three‑dimensional inverse scattering question.

Along with foundational conventions and notation, the text presents an integral transform theorem and the role of the spectral weight operator in linking data to the underlying kernel. It discusses how a scattering operator can encapsulate essential information and what conditions can guarantee unique recovery of the system’s kernel from partial knowledge of the scattering operator. The material is aimed at readers with interest in mathematical physics and applied analysis of wave phenomena.

• Understand the physical setup and the goal of determining a kernel from scattering data.
• Learn how integral equations, eigenfunctions, and transform theorems are used in inverse problems.
• Explore the role of the spectral weight operator and the scattering operator in reconstruction.
• See how uniqueness conditions are formulated and why they matter for recovery.

Ideal for readers of mathematical physics, applied analysis, and engineering disciplines that use wave scattering to probe materials.

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Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 036456301X
• ISBN 13: 9780364563014
• Binding: Hardcover
• Number of pages: 54