Displaying similar documents to “ n -inner product spaces and projections”

On Müntz rational approximation in multivariables

S. Zhou (1995)

Colloquium Mathematicae

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The present paper shows that for any s sequences of real numbers, each with infinitely many distinct elements, λ n j , j=1,...,s, the rational combinations of x 1 λ m 1 1 x 2 λ m 2 2 . . . x s λ m s s are always dense in C I s .

Geometric study of the beta-integers for a Perron number and mathematical quasicrystals

Jean-Pierre Gazeau, Jean-Louis Verger-Gaugry (2004)

Journal de Théorie des Nombres de Bordeaux

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We investigate in a geometrical way the point sets of   ℝ   obtained by the   β -numeration that are the   β -integers   ℤ β ⊂ ℤ [ β ]   where   β   is a Perron number. We show that there exist two canonical cut-and-project schemes associated with the   β -numeration, allowing to lift up the   β -integers to some points of the lattice   ℤ m   ( m =   degree of   β ) lying about the dominant eigenspace of the companion matrix of   β  . When   β   is in particular a Pisot number, this framework gives another proof of the fact...

On the representation of functions by orthogonal series in weighted L p spaces

M. Grigorian (1999)

Studia Mathematica

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It is proved that if φ n is a complete orthonormal system of bounded functions and ɛ>0, then there exists a measurable set E ⊂ [0,1] with measure |E|>1-ɛ, a measurable function μ(x), 0 < μ(x) ≤ 1, μ(x) ≡ 1 on E, and a series of the form ∑ k = 1 ∞ c k φ k ( x ) , where c k ∈ l q for all q>2, with the following properties: 1. For any p ∈ [1,2) and f ∈ L μ p [ 0 , 1 ] = f : ʃ 0 1 | f ( x ) | p μ ( x ) d x < ∞ there are numbers ɛ k , k=1,2,…, ɛ k = 1 or 0, such that l i m n → ∞ ʃ 0 1 | ∑ k = 1 n ɛ k c k φ k ( x ) - f ( x ) | p μ ( x ) d x = 0 . 2. For every p ∈ [1,2) and f ∈ L μ p [ 0 , 1 ] there are a function g ∈ L 1 [ 0 , 1 ] with g(x) = f(x) on E and numbers δ k , k=1,2,…, δ k = 1 or 0,...