Editing Harmonic analysis (section)

==Other branches==
*Study of the [[eigenvalue]]s and [[eigenvector]]s of the [[Laplacian]] on [[domain (mathematical analysis)|domain]]s, [[manifold]]s, and (to a lesser extent) [[Graph (discrete mathematics)|graph]]s is also considered a branch of harmonic analysis. See, e.g., [[hearing the shape of a drum]].<ref>{{cite book |last1=Terras |first1=Audrey |title=Harmonic Analysis on Symmetric Spaces-Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane |date=2013 |publisher=Springer |location=New York, NY |isbn=978-1461479710 |page=37 |edition=2nd |url=https://books.google.com/books?id=LcHBAAAAQBAJ&q=harmonic+analysis+hear+shape+of+a+drum&pg=PA37 |access-date=12 December 2017}}</ref>
* Harmonic analysis on Euclidean spaces deals with properties of the [[Fourier transform]] on '''R'''<sup>''n''</sup> 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 function]]s and [[spherical harmonic]]s.
* Harmonic analysis on tube domains is concerned with generalizing properties of [[Hardy space]]s 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 [[Operator (mathematics)|operators]] and [[partial differential equations|equations]].<ref>{{cite book | chapter-url=https://www.degruyter.com/document/doi/10.1515/9781400882090-002/html?lang=en | doi=10.1515/9781400882090-002 | chapter=Non-Linear Harmonic Analysis, Operator Theory and P.d.e. | title=Beijing Lectures in Harmonic Analysis. (AM-112) | date=1987 | last1=Coifman | first1=R. R. | last2=Meyer | first2=Yves | pages=1–46 | isbn=978-1-4008-8209-0 }}</ref>