プランシュレルの定理も分からんカスは過疎地に移住してもらったほうがよくね？

知的労働には向いてない

良スレ

プランシェルリの定理って何？

レル

意味を聞いてるんだよ、馬鹿か

>プランシェルリの定理って何？

プランシェレルの定理?

アホが

Plansherel's theorem

Plancherel's theorem, also known as the Parseval–Plancherel identity, is a fundamental result in harmonic analysis, proven by Michel Plancherel in 1910. It generalizes Parseval's theorem and is widely used in science and engineering to prove the unitarity of the Fourier transform.

The theorem states that the integral of a function's squared modulus is equal to the integral of the squared modulus of its frequency spectrum. Mathematically, if ( f ) is a function on the real line and ( \widehat{f} ) is its frequency spectrum, then:

[ \int_{-\infty}^{\infty} |f(x)|^2 , dx = \int_{-\infty}^{\infty} |\widehat{f}(\xi)|^2 , d\xi ]

A more precise formulation is that if a function is in both ( L^p ) spaces and ( L^2 ), then its Fourier transform is in ( L^2 ) and the Fourier transform is an isometry with respect to the ( L^2 ) norm. This implies that the Fourier transform restricted to ( L^2 ) has a unique extension to a linear isometric map, sometimes called the Plancherel transform.

Harish-Chandra's Plancherel theorem
one of the deepest theorems in the 20 century

On Harish-Chandra's Plancherel theorem for Riemannian symmetric spaces
Bernhard Krötz, Job J. Kuit, Henrik Schlichtkrull