- Parseval equality
- равенство Парсеваля
English-russian dictionary of physics. 2013.
Parseval equality
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Parseval's identity — In mathematical analysis, Parseval s identity is a fundamental result on the summability of the Fourier series of a function. Geometrically, it is the Pythagorean theorem for inner product spaces. Informally, the identity asserts that the sum of… … Wikipedia
Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… … Wikipedia
Fourier transform — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms The Fourier transform is a mathematical operation that decomposes a function into its constituent… … Wikipedia
Discrete Fourier transform — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms In mathematics, the discrete Fourier transform (DFT) is a specific kind of discrete transform, used in… … Wikipedia
Inner product space — In mathematics, an inner product space is a vector space with the additional structure of inner product. This additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors.… … Wikipedia
Pythagorean theorem — See also: Pythagorean trigonometric identity The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c) … Wikipedia
Wirtinger's inequality for functions — For other inequalities named after Wirtinger, see Wirtinger s inequality. In mathematics, historically Wirtinger s inequality for real functions was an inequality used in Fourier analysis. It was named after Wilhelm Wirtinger. It was used in 1904 … Wikipedia
Fourier analysis — In mathematics, Fourier analysis is a subject area which grew out of the study of Fourier series. The subject began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions. The… … Wikipedia
Generalized Fourier series — In mathematical analysis, many generalizations of Fourier series have proved to be useful.They are all special cases of decompositions over an orthonormal basis of an inner product space.Here we consider that of square integrable functions… … Wikipedia
Bessel's inequality — In mathematics, especially functional analysis, Bessel s inequality is a statement about the coefficients of an element x in a Hilbert space with respect to an orthonormal sequence.Let H be a Hilbert space, and suppose that e 1, e 2, ... is an… … Wikipedia
