#harmonic-analysis
43. Abstract Harmonic Analysis
This volume extends harmonic analysis to general locally compact groups. It replaces classical Fourier series and transforms with representation-theoretic and measure-theoretic frameworks. Part I. Locally Compact Groups Chapter 1. Topological Groups 1.1 Definitions and examples 1.2 Continuity and group operations 1.3 Subgroups and quotient groups 1.4 Compact and locally compact groups 1.5 Examples Chapter 2. Haar Measure 2.1 Existence and uniqueness 2.2 Left and right invariance 2.3 Integration on groups...
42. Harmonic Analysis
This volume studies representation of functions via oscillatory components such as Fourier series and transforms. It connects analysis, PDEs, number theory, and signal processing. Part I. Fourier Analysis on ℝ Chapter 1. Fourier Transform 1.1 Definition 1.2 Basic properties 1.3 Inversion formula 1.4 Plancherel theorem 1.5 Examples Chapter 2. Convolution 2.1 Definition 2.2 Properties 2.3 Convolution theorem 2.4 Approximate identities 2.5 Applications Chapter 3. Distributions (Overview) 3.1 Generalized functions 3.2...