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mathematics, the Plancherel theorem (sometimes called the Parseval–Plancherel identity) is a result in harmonic analysis, proven by Michel Plancherel in 1910....

Michel Plancherel (French pronunciation: [miʃɛl plɑ̃ʃʁɛl]; 16 January 1885 – 4 March 1967) was a Swiss mathematician. He was born in Bussy (Canton of Fribourg...

In mathematics, Plancherel measure is a measure defined on the set of irreducible unitary representations of a locally compact group G {\displaystyle G}...

In mathematics, the Plancherel theorem for spherical functions is an important result in the representation theory of semisimple Lie groups, due in its...

{\displaystyle |f|_{2}={\sqrt {|S|}},} we get a contradiction with the Plancherel identity | f ^ | 2 = | f | 2 {\displaystyle |{\widehat {f}}|_{2}=|f|_{2}}...

Cécile Plancherel (born 28 October 1970) is a Swiss snowboarder. She competed at the 1998 Winter Olympics, in giant slalom. Evans, Hilary; Gjerde, Arild;...

The Plancherel–Rotach asymptotics are asymptotic results for orthogonal polynomials. They are named after the Swiss mathematicians Michel Plancherel and...

topology. The analogue of the Plancherel theorem is abstractly given by identifying a measure on the unitary dual, the Plancherel measure, with respect to...

{g}}(\xi )}}\,d\xi ,} where the bar denotes complex conjugation. The Plancherel theorem, which follows from the above, states that ‖ f ‖ L 2 2 = ∫ − ∞...

physics, the most general form of this property is more properly called the Plancherel theorem. Suppose that A ( x ) {\displaystyle A(x)} and B ( x ) {\displaystyle...

For functions f , g : G → C {\displaystyle f,g:G\to \mathbb {C} } , the Plancherel formula states ∑ a ∈ G f ( a − 1 ) g ( a ) = 1 | G | ∑ i d ϱ i Tr ( f...

A Fourier series (/ˈfʊrieɪ, -iər/) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a...

that their Hankel transforms Fν(k) and Gν(k) are well defined, then the Plancherel theorem states ∫ 0 ∞ f ( r ) g ( r ) r d r = ∫ 0 ∞ F ν ( k ) G ν ( k )...

_{k=0}^{N-1}X_{k}Y_{k}^{*}} where the star denotes complex conjugation. The Plancherel theorem is a special case of Parseval's theorem and states: ∑ n = 0 N...

\mathbb {R} } with α < c < β {\displaystyle \alpha <c<\beta } . Then the Plancherel theorem holds: ∫ − ∞ ∞ e − 2 c t | f ( t ) | 2 d t = 1 2 π ∫ − ∞ ∞ | F...

operator between two principal series representations, that appears in the Plancherel measure for semisimple Lie groups. Harish-Chandra (1958a, 1958b) introduced...

This dual object is suitable for formulating a Fourier transform and a Plancherel theorem for unimodular separable locally compact groups of type I and...

π , π ] . {\displaystyle L^{2}[-\pi ,\pi ].} A similar result is the Plancherel theorem, which asserts that the integral of the square of the Fourier...

necessarily isometric on L 2 {\displaystyle L^{2}} spaces. See below at Plancherel and L2 Fourier inversion theorems. The space of integrable functions on...

H_{k}(x)} is the k {\displaystyle k} th Hermite polynomial. The poissonized Plancherel measure on integer partition (and therefore on Young diagramss) plays...