Matches in DBpedia 2014 for { ?s ?p In mathematical analysis, Parseval's identity, named after Marc-Antoine Parseval, is a fundamental result on the summability of the Fourier series of a function. Geometrically, it is thePythagorean theorem for inner-product spaces. Informally, the identity asserts that the sum of the squares of the Fourier coefficients of a function is equal to the integral of the square of the function, where the Fourier coefficients cn of ƒ are given byMore formally, the result holds as stated provided ƒ is square-integrable or, more generally, in L2[−π,π]. A similar result is the Plancherel theorem, which asserts that the integral of the square of the Fourier transform of a function is equal to the integral of the square of the function itself. In one-dimension, for ƒ ∈ L2(R),. }
Showing items 1 to 1 of
1
with 100 items per page.
- Parseval's_identity abstract "In mathematical analysis, Parseval's identity, named after Marc-Antoine Parseval, is a fundamental result on the summability of the Fourier series of a function. Geometrically, it is thePythagorean theorem for inner-product spaces. Informally, the identity asserts that the sum of the squares of the Fourier coefficients of a function is equal to the integral of the square of the function, where the Fourier coefficients cn of ƒ are given byMore formally, the result holds as stated provided ƒ is square-integrable or, more generally, in L2[−π,π]. A similar result is the Plancherel theorem, which asserts that the integral of the square of the Fourier transform of a function is equal to the integral of the square of the function itself. In one-dimension, for ƒ ∈ L2(R),".