Hilbert Space Methods in Signal Processing
1st Edition
Published on 16. April 2013
978-1-107-33084-9 (ISBN)
Description
This lively and accessible book describes the theory and applications of Hilbert spaces and also presents the history of the subject to reveal the ideas behind theorems and the human struggle that led to them. The authors begin by establishing the concept of 'countably infinite', which is central to the proper understanding of separable Hilbert spaces. Fundamental ideas such as convergence, completeness and dense sets are first demonstrated through simple familiar examples and then formalised. Having addressed fundamental topics in Hilbert spaces, the authors then go on to cover the theory of bounded, compact and integral operators at an advanced but accessible level. Finally, the theory is put into action, considering signal processing on the unit sphere, as well as reproducing kernel Hilbert spaces. The text is interspersed with historical comments about central figures in the development of the theory, which helps bring the subject to life.
Reviews / Votes
'A book of this mathematical sophistication shouldn't be this fun to read - or teach from! Guilty pleasure aside, the treatment of Hilbert spaces and operator theory is remarkable in its lucidity and completeness - several other textbooks' worth of material. More than half of the book consists of new insights into spherical data analysis cast in a general framework that will make any of us working in this and adjacent research areas reach for this book to properly understand what it is that we have done.' Frederik J. Simons, Princeton University 'The style is lively, and the mathematics is interspersed with historical remarks and anecdotes about the main mathematicians who developed the theory ... some insights are given that can [be] enlightening for professionals as well.' A. Blutheel, Mathematical ReviewsMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 15 Tables, black and white; 66 Line drawings, unspecified
File size
67457,56 MB
ISBN-13
978-1-107-33084-9 (9781107330849)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Rodney A. Kennedy | Parastoo Sadeghi
Hilbert Space Methods in Signal Processing
Book
03/2013
Cambridge University Press
€194.80
Shipment within 15-20 days
Persons
Rodney Kennedy is a Professor in the Research School of Engineering and the Head of the Applied Signal Processing research group at the Australian National University. He has won a number of prizes in engineering and mathematics, including UNSW University and ATERB Medals. He has supervised more than 40 PhD students and co-authored approximately 300 research papers. He is a Fellow of the IEEE. Parastoo Sadeghi is a Fellow in the Research School of Engineering at the Australian National University. She has published around 70 refereed journal and conference papers and received two IEEE Region 10 paper awards. She is a Senior Member of the IEEE.
Content
Part I. Hilbert spaces: 1. Introduction; 2. Spaces; Part II. Operators: 3. Introduction to operators; 4. Bounded operators; 5. Compact operators; 6. Integral operators; Part III. Applications: 7. Signals and systems analysis on the 2-sphere; 8. Signal concentration and joint spatio-spectral analysis; 9. Convolution on 2-sphere; 10. Reproducing kernel Hilbert spaces.
