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Arbitrarily Sparse Spectra for Self-Affine Spectral Measures
Given an expansive matrix R ∈ M d (ℤ) and a finite set of digit B taken from ℤ d / R ( ℤ d ). It was shown previously that if we can find an L such that ( R,...
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Frame approximation with bounded coefficients
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a...
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On Excess of Retro Banach Frames
The excess of a frame is the greatest number of elements that can be removed from a given frame, yet leave a set which is a frame for the underlying...
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Explicit bounds of complex exponential frames on a complex field
In the context of Riesz basis, studies on classical system of exponentials find their origin in the celebrated 1934’s work of Paley and Wiener. The...
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Weaving
K -Frames in Hilbert SpacesGǎvruta introduced K -frames for Hilbert spaces to study atomic systems with respect to a bounded linear operator. There are many differences between K ...
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Greedy Algorithms and Approximation Properties for Frames in Hilbert Spaces
We study the Threshold Greedy Algorithm (TGA) and Orthogonal Greedy Algorithm (OGA) for frames in Hilbert spaces and obtain various approximation...
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Number Theoretic Considerations Related to the Scaling of Spectra of Cantor-Type Measures
We investigate some relations between number theory and spectral measures related to the harmonic analysis of a Cantor set. Specifically, we explore...
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Generalized Weaving Frames for Operators in Hilbert Spaces
This paper studies weaving properties of a family of operators which are analysis and synthesis systems with frame-like properties for closed...
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Frames and non linear approximations in Hilbert spaces
A simple proof of the proposition, stated in ([2], p. 346), asserting that in Hilbert spaces a Riesz basis is greedy, is given. Also, greedy...
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Nonstationary Gabor frames - approximately dual frames and reconstruction errors
Nonstationary Gabor frames, recently introduced in adaptive signal analysis, represent a natural generalization of classical Gabor frames by allowing...
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Irregular multiresolution analysis and associated wavelet
We introduce two generalizations, the first of which generalizes the concept of multiresolution analysis. We define the irregular generalized...
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Closure of dilates of shift-invariant subspaces
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...
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Nonuniform Sampling and Recovery of Multidimensional Bandlimited Functions by Gaussian Radial-Basis Functions
Let S ⊂ℝ d be a bounded subset with positive Lebesgue measure. The Paley-Wiener space associated to S , PW S , is defined to be the set of all...
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Frequency-Scale Frames and the Solution of the Mexican Hat Problem
We resolve a long-standing question on L p completeness of the time-scale (or wavelet) system generated by the Mexican hat function, when p ≥2.
Our...
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The Method of Virtual Components in the Multivariate Setting
We describe the so-called method of virtual components for tight wavelet framelets to increase their approximation order and vanishing moments in the...
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Poisson Type Generators for L 1(ℝ)
We characterize the discrete sets Λ⊆ℝ such that { φ ( t − λ ), λ ∈Λ} span L 1 (ℝ), φ being an L 1 (ℝ)-function whose Fourier transform behaves like e ...