In mathematics, especially functional analysis, Bessel's inequality is a statement about the coefficients of an element x {\displaystyle x} {\displaystyle x} ...

A monotonicity property of Bessel's inequality in inner product spaces is given. 1. Introduction. Let X be a linear space over the real or complex number field ...

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 ...

9 мая 2022 г. · The geometric meaning of Bessel's inequality is that the orthogonal projection of an element f on the linear span of the elements ϕα, α∈A, has a ...

30 окт. 2022 г. · Theorem. Let (V,⟨⋅,⋅⟩) be an inner product space. Let ‖⋅‖ be the inner product norm for (V,⟨⋅,⋅⟩). Let E={en:n∈N} be a countably infinite ...

If they are a complete orthogonal system, then the inequality (2) becomes an equality, so (6) becomes an equality and is known as Parseval's theorem.

28 июн. 2011 г. · Bessel's inequality governs inner product spaces, by showing that the hypotenuse of triangles is always at least as long as its cosine ... Bessel's (in)equality confusion -- always an equality? Bessels inequality proof - linear algebra - Math Stack Exchange Proving Bessel's Inequality, with equality if and only if - u linear algebra - The concept/physical meaning/interpretations ... Другие результаты с сайта math.stackexchange.com

22 мар. 2013 г. · The inequality means that the series converges. For a complete orthonormal series, we have Parseval's theorem, which replaces ...

Let us consider the problem of the best approximation of a vector x by vectors of an orthonormal system from a Hilbert space X. For every system of numbers ...