Results 41 to 50 of about 8,503 (184)

A note on exponential Riesz bases

Sampling Theory, Signal Processing, and Data Analysis, 2022
AbstractWe prove that if$$I_\ell = [a_\ell ,b_\ell )$$Iℓ=[aℓ,bℓ),$$\ell =1,\ldots ,L$$ℓ=1,…,L, are disjoint intervals in [0, 1) with the property that the numbers$$1, a_1, \ldots , a_L, b_1, \ldots , b_L$$1,a1,…,aL,b1,…,bLare linearly independent over$${\mathbb {Q}}$$Q, then there exist pairwise disjoint sets$$\Lambda _\ell \subset {\mathbb {Z}}$$Λℓ⊂Z,$
Andrei Caragea, Dae Gwan Lee
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Hamiltonians with Riesz Bases of Generalised Eigenvectors and Riccati Equations [PDF]

, 2010
An algebraic Riccati equation for linear operators is studied, which arises in systems theory. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. To this end, invariant graph subspaces
Wyss, Christian
core   +1 more source

Weaving Riesz Bases

Journal of Fourier Analysis and Applications
This paper explores woven frames in separable Hilbert spaces with an initial focus on the finite-dimensional case. We begin by simplifying the problem to bases, for which we obtain a unique characterization. We establish a condition that is both necessary and sufficient for vector reconstruction, which applies to Fourier matrices.
C. Cabrelli, U. Molter, F. Negreira
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Fractal Frames of Functions on the Rectangle

Fractal and Fractional, 2021
In this paper, we define fractal bases and fractal frames of L2(I×J), where I and J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification of L2(I×J) with the ...
María A. Navascués, Ram Mohapatra, Md. Nasim Akhtar   +2 more
doaj   +1 more source

Perturbations of frames

, 2013
In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames.
Chen, Dongyang, Li, Lei, Zheng, Bentuo
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Mathematical aspects of intertwining operators: the role of Riesz bases [PDF]

, 2010
In this paper we continue our analysis of intertwining relations for both self-adjoint and not self-adjoint operators. In particular, in this last situation, we discuss the connection with pseudo-hermitian quantum mechanics and the role of Riesz bases ...
Ali S T Bagarello F Gazeau J-P, Bagarello F, Bagarello F, Bagarello F, Christensen O, Cooper F, F Bagarello, Junker G, Mostafazadeh A, Mostafazadeh A, Reed M, Trifonov D A, Young R   +12 more
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Characterizing the R-duality of g-frames

Journal of Inequalities and Applications, 2019
In this paper, we define the g-Riesz-dual of a given special operator-valued sequence with respect to g-orthonormal bases for a separable Hilbert space.
Liang Li, Pengtong Li
doaj   +1 more source

Binary Operations in Metric Spaces Satisfying Side Inequalities

Mathematics, 2021
The theory of metric spaces is a convenient and very powerful way of examining the behavior of numerous mathematical models. In a previous paper, a new operation between functions on a compact real interval called fractal convolution has been introduced.
María A. Navascués, Pasupathi Rajan, Arya Kumar Bedabrata Chand   +2 more
doaj   +1 more source

p-Riesz bases in quasi shift invariant spaces

, 2017
Let $ 1\leq p< \infty$ and let $\psi\in L^{p}(\R^d)$. We study $p-$Riesz bases of quasi shift invariant spaces $V^p(\psi;Y)$
De Carli, Laura, Vellucci, Pierluigi
core   +1 more source

Linear combinations of frame generators in systems of translates [PDF]

, 2013
A finitely generated shift invariant space $V$ is a closed subspace of $L^2(\R^d)$ that is generated by the integer translates of a finite number of functions.
Cabrelli, Carlos, Mosquera, Carolina A., Paternostro, Victoria   +2 more
core   +2 more sources