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:
“What are the roots that clutch, what branches grow
Out of this stony rubbish?”
—T.S. (Thomas Stearns)
““I couldn’t afford to learn it,” said the Mock Turtle with a sigh. “I only took the regular course.”
“What was that?” inquired Alice.
“Reeling and Writhing, of course, to begin with,” the Mock Turtle replied; “and then the different branches of Arithmetic—Ambition, Distraction, Uglification, and Derision.”
“I never heard of ‘Uglification,’” Alice ventured to say.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
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