This is a mathematical book on Fourier analysis. The aim is to present the basic notions and techniques of Fourier analysis in discrete settings, thus opening up this area of mathematics to a wide readership. The book consists of twoparts. The first thirteen chapters contain topics related to the finite Fourier transform that can be completely understood by undergraduate students with basic knowledge of linear algebra and calculus. The last ten chapters are built on Hilbert spaces and Fourier series. Notwithstanding the use of the language of measure theory in the second part of the book, much of the contents are accessible to students familiar with an undergraduate course in real analysis. An average graduate student in mathematics should be able to benefit from the entire book and hence equipped to do research in this subject. The mathematical notions are presented both on a basic level, making thus the content accessible to a wide audience, and later on, on a more sophisticated level, which can bring students more effectively to the frontier of research Pseudo-differential operators are presented in the perspectives of signal analysis Exercises are included to enhance the use of the book as a textbookIncludes introduction to wavelets and to pseudo-differential operators INDICE: Preface. The Finite Fourier Transform. Translation-Invariant Linear Operators. Circulant Matrices. Convolution Operators. Fourier Multipliers. Eigenvalues and Eigenfunctions. The Fast Fourier Transform. Time-Frequency Analysis. Time-Frequency Localized Bases. Wavelet Transforms and Filter Banks. Haar Wavelets. Daubechies Wavelets. The Trace. Hilbert Spaces. Bounded Linear Operators. Self-Adjoint Operators. Compact Operators. The Spectral Theorem. Schatten–von Neumann Classes. Fourier Series. Fourier Multipliers on S1.Pseudo-Differential Operators on S1. Pseudo-Differential Operatorson Z. Bibliography. Index.
- ISBN: 978-3-0348-0115-7
- Editorial: Springer Basel
- Encuadernacion: Rústica
- Páginas: 180
- Fecha Publicación: 01/07/2011
- Nº Volúmenes: 1
- Idioma: Inglés