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This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis.   The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis.   Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.

Fourier analysis. --- Fourier analysis --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Analysis, Fourier --- Mathematics. --- Harmonic analysis. --- Partial differential equations. --- Numerical analysis. --- Fourier Analysis. --- Abstract Harmonic Analysis. --- Partial Differential Equations. --- Numerical Analysis. --- Mathematical analysis --- Differential equations, partial. --- Partial differential equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Differential equations, Partial.

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This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the session and invited papers by experts in fields that involve pseudo-differential operators. The first four chapters focus on the functional analysis of pseudo-differential operators on a spectrum of settings from Z to Rn to compact groups. Chapters 5 and 6 discuss operators on Lie groups and manifolds with edge, while the following two chapters cover topics related to probabilities. The final chapters then address topics in differential equations.

Pseudodifferential operators. --- Operators, Pseudodifferential --- Pseudo-differential operators --- Operator theory --- Differential equations, partial. --- Operator theory. --- Functional analysis. --- Partial Differential Equations. --- Operator Theory. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functional analysis --- Partial differential equations --- Partial differential equations.

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Consists of seventeen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at the Middle East Technical University in Ankara, Turkey on August 13-18, 2007.

Differential equations, Partial. --- Pseudodifferential operators. --- Mathematics. --- Pseudodifferential operators --- Differential equations, Partial --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Operator theory. --- Operators, Pseudodifferential --- Pseudo-differential operators --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Partial differential equations. --- Operator Theory. --- Partial Differential Equations. --- Global Analysis and Analysis on Manifolds. --- Functional analysis --- Operator theory --- Differential equations, partial. --- Global analysis. --- Partial differential equations --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic