Some Uniqueness Theorems for the Reduced Wave Equation (Classic Reprint)
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
£ 14.26
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Print on Demand. This book completes and extends the Magnus-Rellich uniqueness theorem for the reduced wave equation in infinite domains, including piece-wise smooth boundaries and mixed boundary conditions. No auxiliary "edge conditions" are required at edges or discontinuities in the boundary conditions; continuity of the wave function in the closure of the domain is sufficient. This extension allows several interesting problems in diffraction theory, such as diffraction by a disk of zero thickness or a semi-infinite circular cone. The original uniqueness theorem for the reduced wave equation in infinite domains was stated by Sommerfeld, and first proved by Magnus. The elimination of an extraneous "finiteness condition" was accomplished by Rellich, resulting in the theorem stated above. The author extends the theorem to include a considerably more general class of finite boundaries and infinite boundaries, and boundaries with singularities of the type occurring at the apex of a (generalized) cone. The extension to infinite boundaries is limited to the case where the domain is "eventually conical", i.e. outside a sufficiently large sphere, it is generated by a ray emanating from the center. This book represents a significant contribution to the field of diffraction theory, providing a more general and flexible framework for analyzing wave phenomena in complex domains. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.…
Seller Inventory # 9781330155424_0
- Title
- Some Uniqueness Theorems for the Reduced Wave Equation (Classic Reprint)
- Author
- Leo M. Levine
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1330155424
- ISBN 13
- 9781330155424
- Seller catalogs
- Calculus
The general mixed boundary value problem in diffraction theory has apparently not been considered elsewhere, although some special problems have been investi gated. The third boundary value problem (for smooth surfaces) was treated by Leis [12] Regarding infinite boundaries, Peters and Stoker proved uniqueness for the case of a boundary in two dimensions which consists, eventually, of two straight lines extending to infinity. For the case of real k, the extension of the unique ness theorem to infinite boundaries presented here treats the three dimensional analogues of the infinite boundaries of [?fl, namely, eventually conical boundaries. However, in the three dimensional case, where the cones have arbitrary shapes they may have edges extending to infinity) and where mixed boundary condi tions are considered, the proof; although along lines similar to that of [b.
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Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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Forgotten Books publishes hundreds of thousands of rare and classic books.
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value.
The digital edition of all books may be viewed before purchase if you request a sample.
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