Other branches Study of the eigenvalues and eigenvectors of the Laplacian on domains, manifolds, and (to a lesser extent) graphs is also considered a branch of harmonic analysis. See, e.g., hearing the shape of a drum. Harmonic analysis on Euclidean spaces deals with properties of the Fourier transform on Rn that have no analog on general groups. For example, the fact that the Fourier transform is rotation-invariant. Decomposing the Fourier transform into its radial and spherical components leads to topics such as Bessel functions and spherical harmonics. Harmonic analysis on tube domains is concerned with generalizing properties of Hardy spaces to higher dimensions. Automorphic forms are generalized harmonic functions, with respect to a symmetry group. They are an old and at the same time active area of development in harmonic analysis due to their connections to the Langlands program. Non linear harmonic analysis is the use of harmonic and functional analysis tools and techniques to study nonlinear systems. This includes both problems with infinite degrees of freedom and also non linear operators and equations.
Other branches Study of the eigenvalues and eigenvectors of the Laplacian on domains manifolds and (to a lesser extent) graphs is also considered a branch of harmonic analysis See eg hearing the shape of a drum Harmonic analysis on Euclidean spaces deals with properties of the Fourier transform on Rn that have no analog on general groups For example the fact that the Fourier transform is rotation-invariant Decomposing the Fourier transform into its radial and spherical components leads to topics such as Bessel functions and spherical harmonics Harmonic analysis on tube domains is concerned with generalizing properties of Hardy spaces to higher dimensions Automorphic forms are generalized harmonic functions with respect to a symmetry group They are an old and at the same time active area of development in harmonic analysis due to their connections to the Langlands program Non linear harmonic analysis is the use of harmonic and functional analysis tools and techniques to study nonlinear systems This includes both problems with infinite degrees of freedom and also non linear operators and equations