Related papers: Tiling functions and Gabor orthonormal basis
Motivated by a recent generalization of the Balian-Low theorem and by new research in wireless communications we analyze the construction of Wilson bases for general time-frequency lattices. We show that orthonormal Wilson bases for $\LtR$…
We show that the Wirtinger criterion cannot be used to investigate the frame set conjecture for the first Hermite function. More generally, for odd functions, it cannot determine regions of the frame set with density less than 2.
Let $\Omega_1,\Omega_2$ be two disjoint open sets in $\mathbf C^n$ whose boundaries share a smooth real hypersurface $M$ as relatively open subsets. Assume that $\Omega_i$ is equipped with a complex structure $J^i$ which is smooth up to…
The goal of this paper is to introduce and study some geometric properties of slice regular functions of quaternion variable like univalence, subordination, starlikeness, convexity and spirallikeness in the unit ball. We prove a number of…
We do further investigation in a certain cosine function defined for smooth Minkowski spaces. We prove that such function is symmetric if and only if the referred space is Euclidean, and also that it can be given in terms of the Gateaux…
The examples of rhythmical signals with variable period are considered. The definition of periodic function with the variable period is given as a model of such signals. The examples of such functions are given and their variable periods…
We give improvements of the deformation method for computing the zeta function of a generic projective hypersurface in characteristic~$p$ that either reduce the dependence on~$p$ of the time complexity to $\tilde{O}(p^{1/2})$ or that of the…
Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual…
Certain Bernoulli convolution measures (\mu) are known to be spectral. Recently, much work has concentrated on determining conditions under which orthonormal Fourier bases (i.e. spectral bases) exist. For a fixed measure known to be…
In a recent paper in Appl. Comput. Harmon. Anal. 38(2), 196--221 (2014) we have introduced and studied the notion of weak Hamiltonian deformation of a Gabor (=Weyl-Heisenberg) frame. In this Note we use these results to prove that one can…
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…
This survey offers a systematic and streamlined exposition of the most important characterizations of Gabor frames over a lattice. The goal is to collect the most important characterizations of Gabor frames and offer a systematic exposition…
For gapped periodic systems (insulators), it has been established that the insulator is topologically trivial (i.e., its Chern number is equal to $0$) if and only if its Fermi projector admits an orthogonal basis with finite second moment…
This study aims on proposing a new structure for constructing Bernstein-like bases. The structure uses an auxiliary function and a shape parameter to construct a new family of bases from any family of blending functions. The new family of…
Serre and Stark found a basis for the space of modular forms of weight 1/2 in terms of theta series. In this paper, we generalize their result - under certain mild restrictions on the level and character - to the case of weight 1/2 Hilbert…
We show that there exist two dimensional (2D) time reversal invariant fractionalized insulators with the property that both their boundary with the vacuum and their boundary with a topological insulator can be fully gapped without breaking…
We consider tilings $(\mathcal{Q},\Phi)$ of $\mathbb{R}^d$ where $\mathcal{Q}$ is the $d$-dimensional unit cube and the set of translations $\Phi$ is constrained to lie in a pre-determined lattice $A \mathbb{Z}^d$ in $\mathbb{R}^d$. We…
Gabor frames have interested many mathematicians and physicists due to their potential applications in time-frequency analysis, in particular, signal processing. A Gabor system is a collection of vectors which is obtained by applying…
Conway and Lagarias showed that certain roughly triangular regions in the hexagonal grid cannot be tiled by shapes Thurston later dubbed tribones. Here we study a two-parameter family of roughly hexagonal regions in the hexagonal grid and…
Generalized Z_k^(r/2) parafermionic theories - characterized by the dimension (r/2)(1-1/k) of the basic parafermionic field - provide potentially interesting quantum-Hall trial wavefunctions. Such wavefunctions reveal a W_k structure. This…