Top 10 similar words or synonyms for plancherel_theorem

riemann_roch_theorem    0.836819

cauchy_integral_formula    0.834016

uniformization_theorem    0.830514

mellin_transform    0.825011

hilbert_transform    0.821639

serre_duality    0.820506

parseval_theorem    0.820349

hahn_banach_theorem    0.818643

cauchy_schwarz_inequality    0.818623

symmetrization    0.815080

Top 30 analogous words or synonyms for plancherel_theorem

Article Example
Plancherel theorem In mathematics, the Plancherel theorem is a result in harmonic analysis, proven by Michel Plancherel in 1910. It states that the integral of a function's squared modulus is equal to the integral of the squared modulus of its frequency spectrum.
Plancherel theorem A more precise formulation is that if a function is in both "L"(R) and "L"(R), then its Fourier transform is in "L"(R), and the Fourier transform map is an isometry with respect to the "L" norm. This implies that the Fourier transform map restricted to "L"(R) ∩ "L"(R) has a unique extension to a linear isometric map "L"(R) → "L"(R). This isometry is actually a unitary map. In effect, this makes it possible to speak of Fourier transforms of quadratically integrable functions.
Plancherel theorem Plancherel's theorem remains valid as stated on "n"-dimensional Euclidean space R. The theorem also holds more generally in locally compact abelian groups. There is also a version of the Plancherel theorem which makes sense for non-commutative locally compact groups satisfying certain technical assumptions. This is the subject of non-commutative harmonic analysis.
Plancherel theorem The unitarity of the Fourier transform is often called Parseval's theorem in science and engineering fields, based on an earlier (but less general) result that was used to prove the unitarity of the Fourier series.
Plancherel theorem for spherical functions "C"("K" \"G"/"K"), consisting of compactly supported "K"-biinvariant continuous functions on "G", acts by convolution on the Hilbert space "H"="L"("G" / "K"). Because "G" / "K" is a symmetric space, this *-algebra is commutative. The closure of its (the Hecke algebra's) image in the operator norm is a non-unital commutative C* algebra formula_1, so by the Gelfand isomorphism can be identified with the continuous functions vanishing at infinity on its spectrum "X". Points in the spectrum are given by continuous *-homomorphisms of formula_1 into C, i.e. characters of formula_1.