The general forms of these entities are decompositions of a vector in the irreducible representations of a group on a vector space. The convolution of coefficients in one of these objects is given by Parsival's theorem, which also dictates their convergence properties. One form of these is applicable to harmonic functions in a cylinder and has the name Bessel appended to their familiar name. The best-known type of these uses circle group irreps, functions of the form e to the i theta, as basis elements, and is thus a decomposition of a periodic function into a linear superposition of sines and
The general forms of these entities are decompositions of a vector in the irreducible representations of a group on a vector space. The convolution of coefficients in one of these objects is given by Parsival's theorem, which also dictates their convergence properties. One form of these is applicable to harmonic functions in a cylinder and has the name Bessel appended to their familiar name. The best-known type of these uses circle group irreps, functions of the form e to the i theta, as basis elements, and is thus a decomposition of a periodic function into a linear superposition of sines and cosines. For 10 points, name this sum named for a French mathematician.
The general forms of these entities are decompositions of a vector in the irreducible representations of a group on a vector space.
{Fourier series} [or {Fourier decomposition}s]