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Closure of dilates of shift-invariant subspaces

100%

Soto-Bajo M.

Open Mathematics

2013

tom 11

nr 10

1785-1799

Let V be any shift-invariant subspace of square summable functions. We prove that if for some A expansive dilation V is A-refinable, then the completeness property is equivalent to several conditions on the local behaviour at the origin of the spectral function of V, among them the origin is a point of A*-approximate continuity of the spectral function if we assume this value to be one. We present our results also in a more general setting of A-reducing spaces. We also prove that the origin is a point of A*-approximate continuity of the Fourier transform of any semiorthogonal tight frame wavelet if we assume this value to be zero.

On the almost monotone convergence of sequences of continuous functions

86%

Grande Z.

Open Mathematics

2011

tom 9

nr 4

772-777

A sequence (f n)n of functions f n: X → ℝ almost decreases (increases) to a function f: X → ℝ if it pointwise converges to f and for each point x ∈ X there is a positive integer n(x) such that f n+1(x) ≤ f n (x) (f n+1(x) ≥ f n(x)) for n ≥ n(x). In this article I investigate this convergence in some families of continuous functions.

Ograniczanie wyników

2 Open Mathematics

1 Grande Z.

1 Soto-Bajo M.

1 2013

1 2011

Wyniki wyszukiwania

Closure of dilates of shift-invariant subspaces

On the almost monotone convergence of sequences of continuous functions