Quaternion and Clifford Fourier Transforms and Wavelets

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume pr

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Eckhard Hitzer Stephen J. Sangwine Editors

Quaternion and Clifford Fourier Transforms and Wavelets

Trends in Mathematics Trends in Mathematics is a series devoted to the publication of volumes arising from conferences and lecture series focusing on a particular topic from any area of mathematics. Its aim is to make current developments available to the community as rapidly as possible without compromise to quality and to archive these for reference. Proposals for volumes can be submitted using the Online Book Project Submission Form at our website www.birkhauser-science.com. Material submitted for publication must be screened and prepared as follows: All contributions should undergo a reviewing process similar to that carried out by journals and be checked for correct use of language which, as a rule, is English. Articles without proofs, or which do not contain any significantly new results, should be rejected. High quality survey papers, however, are welcome. We expect the organizers to deliver manuscripts in a form that is essentially ready for direct reproduction. Any version of TEX is acceptable, but the entire collection of files must be in one particular dialect of TEX and unified according to simple instructions available from Birkh¨auser. Furthermore, in order to guarantee the timely appearance of the proceedings it is essential that the final version of the entire material be submitted no later than one year after the conference.

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Quaternion and Clifford Fourier Transforms and Wavelets Eckhard Hitzer Stephen J. Sangwine Editors

Editors Eckhard Hitzer Department of Material Science International Christian University Tokyo, Japan

Stephen J. Sangwine School of Computer Science and Electronic Engineering University of Essex Colchester, United Kingdom

ISBN 978-3-0348-0602-2 ISBN 978-3-0348-0603-9 (eBook) DOI 10.1007/978-3-0348-0603-9 Springer Basel Heidelberg New York Dordrecht London Library of Congress Control Number: 2013939066 Mathematics Subject Classification (2010): 11R52, 15A66, 42A38, 65T60, 42C40, 68U10, 94A08, 94A12 © Springer Basel 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always