Related papers: Complete interpolating sequences for the Gaussian …
Several measures for the density of sets of integers have been proposed, such as the asymptotic density, the Schnirelmann density, and the Dirichlet density. There has been some work in the literature on extending some of these concepts of…
In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite-rank approximations…
We extend our work on nonseparated interpolating sequences, originally developed for Bergman spaces with weights of the form $(1 - |z|^2)^\alpha$, to more general weights.
We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as $ \hat g(\xi)= \prod_{j=1}^n (1+2\pi i\delta_j\xi)^{-1}…
Most characterizations of interpolating sequences for Bergman spaces include the condition that the sequence be uniformly discrete in the hyperbolic metric. We show that if the notion of interpolation is suitably generalized, two of these…
We use the supersymmetric formalism to derive an integral formula for the density of states of the Gaussian Orthogonal Ensemble, and then apply saddle-point analysis to give a new derivation of the 1/N-correction to Wigner's law. This…
We provide a description of the interpolating and sampling sequences on a space of holomorphic functions with a uniform growth restriction defined on finite Riemann surfaces.
We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the…
For random piecewise linear systems T of the interval that are expanding on average we construct explicitly the density functions of absolutely continuous T-invariant measures. In case the random system uses only expanding maps our…
A description is given of the image of the Weil representation of the symplectic group in the Schwartz space and in the space of tempered distributions under the Gaussian integral transform. We also discuss the problem of infinite…
We give a characterization of complete interpolating sequences for the Fock spaces $\mathcal{F}^p_\varphi,\ 1\leq p<\infty$, where $\varphi(z)=\alpha\left(\log^+|z|\right)^2,\ \alpha>0$. Our results are {analogous} to the classical…
We characterize interpolating sequences for pairs of reproducing kernels $(s, \ell)$, where $s$ is a complete Pick factor of $\ell.$ This answers a question of Aleman, Hartz, McCarthy and Richter.
We study interpolating sequences of $d$-tuples of matrices, by looking at the commuting and the non-commuting case separately. In both cases, we will give a characterization of such sequences in terms of separation conditions on suitable…
This paper investigates signal prediction through the perfect reconstruction of signals from shift-invariant spaces using nonuniform samples of both the signal and its derivatives. The key advantage of derivative sampling is its ability to…
When we deal with $H^{\infty}$, it is known that $c_0-$interpolating sequences are interpolating and it is sufficient to interpolate idempotents of $\ell_\infty$ in order to interpolate the whole $\ell_\infty$. We will extend these results…
The properties of black-hole and neutron-star binaries are extracted from gravitational-wave signals using Bayesian inference. This involves evaluating a multi-dimensional posterior probability function with stochastic sampling. The…
We characterize sampling and interpolating sets with derivatives in weighted Fock spaces on the complex plane in terms of their weighted Beurling densities.
Gaussian denoising has emerged as a powerful method for constructing simulation-free continuous normalizing flows for generative modeling. Despite their empirical successes, theoretical properties of these flows and the regularizing effect…
The paper study the discrete sets of translations of the Gaussian function that span the spaces L1(R) and L2(R).
We give a description, in analytic and geometric terms, of the interpolation sequences for the algebra of entire functions of exponential type which are bounded on the real line.