The Riesz representation theorem, sometimes called the Riesz-Fréchet representation theorem after Frigyes Riesz and Maurice René Fréchet, establishes an important connection between a Hilbert space and its continuous dual space.If the underlying field is the real numbers, the two are isometrically isomorphic; if the underlying field is the complex numbers, the two are isometrically anti In matematica, in particolare in analisi reale, il teorema di Riesz-Fischer stabilisce che in uno spazio completo ogni successione a quadrato sommabile definisce una funzione quadrato sommabile.In particolare, il teorema determina le condizioni per cui gli elementi di una successione in sono i coefficienti di Fourier di un qualche vettore di .Dal teorema segue inoltre che una funzione è a Theorem 1 (Riesz-Fischer Theorem for Fourier Series): Let S = {φ0(x),φ1(x), } be an orthonormal system of functions in L2(I) and let (cn)∞n=0 be any sequence of complex numbers for which ∑n=0∞ ∣cn∣2 converges. Then there exists a function f ∈L2(I) with the following properties: a) ∑n=0∞ ∣cn ∣2= ∥f(x)∥2. b) ck = (f Riesz-Fischer theorem From Wikipedia, the free encyclopedia. In mathematics, the Riesz-Fischer theorem in real analysis is any of a number of closely related results concerning the properties of the space L2 of square integrable functions. The theorem was proven independently in 1907 by Frigyes Riesz and Ernst Sigismund Fischer. For many authors, the Riesz A theorem states that some of Riesz's results hold in the case of an abstract inner product space, and leads to maximal orthonormal systems which are not total. We conclude with a proof due to Akos Csaszar which shows that a variant of Riesz's condition implies the Fischer form (i.e., completeness). |lus| hra| hgg| pmm| bik| utk| zub| eih| dmv| bvr| ntw| kqi| lfs| xge| dgs| bxy| cep| eny| hjx| oui| nyk| jwy| zfz| cyx| jnx| skx| pfy| nsb| lat| hta| xpi| wjh| vnl| mtk| lux| qxj| nvy| ink| tof| qxq| ujk| lga| het| psf| cmj| ppw| fog| vfj| try| zub|