Related papers: Characterization and computation of canonical tigh…
We prove sharp upper bounds for sums of eigenvalues (and other spectral functionals) of Laplace-like operators, including bi-Laplacian and fractional Laplacian. We show that among linear images of a highly symmetric domain, our spectral…
The exact canonical partition function of a hard disk system in a narrow quasi-one dimensional pore of given length and width is derived analytically in the thermodynamic limit. As a result the many body problem is reduced to solving two…
Let V be a smooth projective 3-fold of general type. Denote by $K^3$, a rational number, the self-intersection of the canonical sheaf of any minimal model of V. One defines $K^3$ as the canonical volume of $V$. Assume $p_g\ge 2$. We show…
For the computational model where only additions are allowed, the $\Omega(n^2\log n)$ lower bound on operations count with respect to image size $n\times n$ is obtained for two types of the discrete Radon transform implementations: the fast…
A Python package for the calculation of spectrograms with optimized time and frequency resolution for application in the analysis of numerical simulations on ultrashort pulse propagation is presented. Gabor's uncertainty principle prevents…
For a matrix $W \in \mathbb{Z}^{m \times n}$, $m \leq n$, and a convex function $g: \mathbb{R}^m \rightarrow \mathbb{R}$, we are interested in minimizing $f(x) = g(Wx)$ over the set $\{0,1\}^n$. We will study separable convex functions and…
In this paper, we propose a novel method for fast face recognition called L1/2 Regularized Sparse Representation using Hierarchical Feature Selection (HSR). By employing hierarchical feature selection, we can compress the scale and…
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…
In this paper we show how to construct a certain class of orthonormal bases in $L^2({\bf R}^d)$ starting from one or more Gabor orthonormal bases in $L^2({\bf R})$. Each such basis can be obtained acting on a single function…
Phase-space features of the Wigner flow for generic one-dimensional systems with a Hamiltonian, $H^{W}(q,\,p)$, constrained by the $\partial ^2 H^{W} / \partial q \partial p = 0$ condition are analytically obtained in terms of Wigner…
Geometrical optics (GO) is widely used for reduced modeling of waves in plasmas but fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different…
We consider existence and uniqueness of symmetric approximation of frames by normalized tight frames and of symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces H . More precisely, we determine whether a given frame…
In the practice, time variable cannot be negative. The space $L^2(\Bbb R_+)$ of square integrable functions defined on the right half real line $\Bbb R_+$ models causal signal space. This paper focuses on a class of dilation-and-modulation…
Let $M$ be a relatively compact $C^2$ domain in a complex manifold $\mathcal M$ of dimension $n$. Assume that $H^{1}(M,\Theta)=0$ where $\Theta$ is the sheaf of germs of holomorphic tangent fields of $M$. Suppose that the Levi-form of the…
In this paper, we provide a direct and constructive proof of weak factorization of $h^1(\mathbb{R})$ (the predual of little BMO space bmo$(\mathbb{R}\times\mathbb{R})$ studied by Cotlar-Sadosky and Ferguson-Sadosky), i.e., for every $f\in…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
The orbit closures of regular model sets generated from a cut-and-project scheme given by a co-compact lattice $\mathcal{L}\subset G\times H$ and compact and aperiodic window $W\subseteq H$, have the maximal equicontinuous factor (MEF)…
In this paper is described the general aspect of a numerical method for piecewise determin-istic Markov processes with boundary. Under very natural hypotheses, a crucial result about uniqueness of solution of a generalized Kolmogorov…
When constructing finite frames for a given application, the most important consideration is the spectrum of the frame operator. Indeed, the minimum and maximum eigenvalues of the frame operator are the optimal frame bounds, and the frame…
Every (full) finite Gabor system generated by a unit-norm vector $g\in \mathbb{C}^d$ is a finite unit-norm tight frame (FUNTF), and can thus be associated with a (Gabor) positive operator valued measure (POVM). Such a POVM is…