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 invariant to rotations. Decomposing the Fourier transform to its radial and spherical components leads to topics such as Bessel functions and spherical harmonics. See the book reference.
- Harmonic analysis on tube domains is concerned with generalizing properties of Hardy spaces to higher dimensions.
Read more about this topic: Harmonic Analysis
Famous quotes containing the word branches:
“Certain branches cut
certain leaves fallen
the grapes
cooked and put up
for winter”
—Denise Levertov (b. 1923)
“...there is hope for a tree, if it is cut down, that it will sprout again, and that its shoots will not cease. Though its root grows old in the earth, and its stump dies in the ground, yet at the scent of water it will bud and put forth branches like a young plant. But mortals die, and are laid low; humans expire, and where are they?”
—Bible: Hebrew, Job 14:7-10.