11 citations · 26 across the 15 of their papers we have counts for
19 papers
Methods of Construction of Exponential Bases on Planar Domains Revised
Oleg Asipchuk, Laura De Carli
In [1], we surveyed classical and recent results on the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We also construc…
Cyclotomy of symmetric polynomials
Laura De Carli, Maurizio Laporta
We prove some new identities for homogeneous symmetric polynomials when evaluated at roots of unity. Some of these formulas are applied to obtain new insights onto cyclotomic polyn…
Block-equivalent finite Gabor frames
Oleg Asipchuk, Laura De Carli, Luis Rodriguez
We study finite systems of vectors whose frame operator matrices are unitarily equivalent, via explicit and computationally efficient unitary transformations, to block-diagonal mat…
Divisibility criteria and coefficient formulas for cyclotomic polynomials
Laura De Carli, Maurizio Laporta
We establish necessary and sufficient conditions for a polynomial to be divisible by a cyclotomic polynomials and derive new formulas involving Ramanujan sums as an application of…
On the Sierpinski triangle and its generalizations
L. De Carli, A. Echezabal, I. Morell
By examining arithmetic operations between decimal numbers in a given base m we uncover fractal structures that generalize the Sierpinski triangle
Methods of construction of exponential bases on planar domains
Oleg Asipchuk, Laura De Carli
In this paper, we survey and refine several results -- some previously established in the literature -- that facilitate the construction of exponential bases on planar domains with…
Concerning the stability of exponential systems and Fourier matrices
Oleg Asipchuk, Laura De Carli, Weilin Li
Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result t…
Approximating the divisor functions
Andrew Echezabal, Laura De Carli, Maurizio Laporta
We exploit the properties of a sequence of functions that approximate the divisor functions and combine them with an analytical formula of a delta-like sequence to give a new proof…
Three problems on exponential bases
Laura De Carli, Alberto Mizrahi, Alexander Tepper
We consider three special and significant cases of the following problem. Let D be a (possibly unbounded) set of finite Lebesgue measure in R^d. Find conditions on D for which the…
Exponential bases on triangular domains
Laura De Carli, Alberto Mizrahi
We construct explicit exponential bases on triangles in R^2 and on infinite unions of segments on the real line.
Stability results for Gabor frames and the p-order hold models
Laura De Carli, Pierluigi Vellucci
We prove stability results for a class of Gabor frames in . We consider window functions in the Sobolev spaces and B-splines of order . Our results ca…
Exponential bases on multi-rectangles in
Laura De Carli
We construct explicit exponential bases on finite unions of disjoint rectangles of with rational vertices.
Pitt inequalities and restriction theorems for the Fourier transform
Laura De Carli, Dmitriy Gorbachev, Sergey Tikhonov
We prove new Pitt inequalities for the Fourier transforms with radial and non-radial weights using weighted restriction inequalities for the Fourier transform on the sphere. We als…
One-parameter groups of operators and discrete Hilbert transforms
Laura De Carli, Gohin Shaikh Samad
We show that the discrete Hilbert transform and the discrete Kak-Hilbert transform are infinitesimal generator of one-parameter groups of operators
Stability of exponential bases on d- dimensional domains
Laura De Carli, Santosh Pathak
We find explicit stability bounds for exponential Riesz bases on domains of R^d. Our results generalize Kadec theorem and other stability theorems in the literature.
Parseval frames with n+1 vectors in R^n
Laura De Carli, Zhongyuan Hu
We construct a Parseval frame with vectors in that contains a given vector. We also provide a characterization of unit-norm frames that can be scaled to a Parseval fra…
Minimal potential results for the Schrodinger equation in a slab
Laura De Carli, Steve Hudson, Xiaosheng Li
Consider the Schrodinger equation -Δu =(k+V) u in an infinite slab S= \R^{n-1}x (0,1), where V is a bounded potential supported on a set D of finite measure. We prove necessary con…
Split functions, Fourier transforms and multipliers
Laura De Carli, Steve Hudson
We study the effect of a splitting operator S_t on the L^p norm of the Fourier transform of a function f and on the operator norm of a Fourier multiplier m. Most of our results ass…
Exponential bases on two dimensional trapezoids
Laura De Carli, Anudeep Kumar
We discuss existence and stability of Riesz bases of exponential type of L^2(T) for special domains T called trapezoids. We construct exponential bases on L^2(T) when T is a finite…