Results 91 to 100 of about 8,384 (123)

Riesz bases by replacement

Sampling Theory, Signal Processing, and Data Analysis, 2022
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Laura De Carli, Julian Edward
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On some riesz bases

Periodica Mathematica Hungarica, 1991
A system of vectors in a Hilbert space \(H\) is a Riesz basis for \(H\) if there is an automorphism of \(H\) carrying the system onto an orthonormal basis for \(H\). The paper under review presents several results which involve Riesz bases either in themselves or in their proofs (or both). The first theorem, proved independently by \textit{M. Horvath} [
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Riesz Bases Multipliers

2013
The paper concerns frame multipliers when one of the involved sequences is a Riesz basis. We determine the cases when the multiplier is well defined and invertible, well defined and not invertible, respectively not well defined.
Diana T. Stoeva, Peter Balazs
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Stability of Riesz bases

Proceedings of the American Mathematical Society, 2018
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Frames versus Riesz Bases

2003
As we have seen, a frame {f k } k=1 ∞ in a Hilbert space H has one of the main properties of a basis: given f ∈ H, there exist coefficients {c k } k=1 ∞ ∈ l 2(ℕ) such that f = ∑ k=1 ∞ c k f k . This makes it natural to study the relationship between frames and bases. We have already seen that Riesz bases are frames.
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Macro-element Hierarchical Riesz Bases

2014
We show that a nested sequence of C r macro-element spline spaces on quasi-uniform triangulations gives rise to hierarchical Riesz bases of Sobolev spaces H s (Ω ...
Oleg Davydov, Wee Ping Yeo
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Weyl-Heisenberg Riesz Bases Generated by Two Intervals

Journal of Fourier Analysis and Applications, 2012
The authors consider Weyl-Heisenberg systems (also called Gabor systems) \[ (g,a,b)=\{ e^{2\pi i m bx} g(x-na) \}_{m, n \in \mathbb Z} \] with \(a=b=1\). They study two problems: I. Characterize the function \(\chi_{E}\), where \(E\) is a union of two separated intervals, so that \((\chi_{E},1,1)\) is a Riesz basis for \(L^{2}(\mathbb R)\).
He, Xing-Gang, Li, Hai-Xiong
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Edge Detection Based on Riesz Transform

2016
In this paper, we present a new way of 2D feature extraction. We start by showing the direct link that exist between the Riesz Transform (RT) and the gradient and Laplacian operators. This formulation allows us to interpret the RT as a gradient of a smoothed image.
Ahror Belaid, Soraya Aloui, Djamal Boukerroui   +2 more
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Perturbation Theorems for Frames and Riesz Bases

Applied Mechanics and Materials, 2013
This paper gives a perturbation theorem for frames in a Hilbert space which is a generalization of a result by Ping Zhao. It is proved that the condition a linear operator is invertible can be weakened to be surjective, and a similar result also be obtained for a Riesz basis.
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Affine Riesz bases and the dual function

Sbornik: Mathematics, 2016
Some parts of the abstract are as follows: ``This paper is concerned with a system of functions on the unit interval which are generated by dyadic dilations and integer translations of a given function. [\dots] Conditions, and in some particular cases, criteria for the generating function are given for the system to be Besselian, to form a Riesz basis ...
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