Related papers: The norm of time-frequency and wavelet localizatio…
This paper studies the regularity problem for block uniformly elliptic operators in divergence form with complex bounded measurable coefficients. We consider the case where the boundary data belongs to Lebesgue spaces with weights in the…
Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise. There is a rich literature establishing the asymptotic normality of rescaled SA iterates under fairly mild conditions. However, these…
With the aim of measuring the sparsity of a real signal, Donoho and Logan introduced the concept of maximum Nyquist density, and used it to extend Bombieri's principle of the large sieve to bandlimited functions. This led to several…
Operator learning, the approximation of mappings between infinite-dimensional function spaces using machine learning, has gained increasing research attention in recent years. Approximate operators, learned from data, can serve as efficient…
For time-frequency localization operators, related to the short-time Fourier transform, with symbol $R\Omega$, we work out the exact large $R$ eigenvalue behavior for rotationally invariant $\Omega$ and conjecture that the same relation…
The sample-function regularity of the random-field solution to a stochastic partial differential equation (SPDE) depends naturally on the roughness of the external noise, as well as on the properties of the underlying integro-differential…
Time-frequency distributions (TFDs) play a vital role in providing descriptive analysis of non-stationary signals involved in realistic scenarios. It is well known that low time-frequency (TF) resolution and the emergency of cross-terms…
Identification of a transient gravitational-wave signal embedded into non-stationary noise requires the analysis of time-dependent spectral components in the resulting time series. The time-frequency distribution of the signal power can be…
We give the first non-trivial upper bounds on the average sensitivity and noise sensitivity of degree-$d$ polynomial threshold functions (PTFs). These bounds hold both for PTFs over the Boolean hypercube and for PTFs over $\R^n$ under the…
We consider an elliptic differential operator $A_\varepsilon = - \frac{d}{dx} g(x/\varepsilon) \frac{d}{dx} + \varepsilon^{-2} V(x/\varepsilon)$, $\varepsilon > 0$, with periodic coefficients acting in $L_2(\mathbb{R})$. For the…
This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly off-the-diagonal and $L^q$-sparse operators with an…
This article presents a mathematical study of the problem of identifying a time-dependent source term in transport processes described by a timefractional parabolic equation, based on noisy time-dependent measurements taken at an arbitrary…
We perform Wigner analysis of linear operators. Namely, the standard time-frequency representation \emph{Short-time Fourier Transform} (STFT) is replaced by the $\mathcal{A}$-\emph{Wigner distribution} defined by $W_{\mathcal A}…
We compute the distribution of the partition functions for a class of one-dimensional Random Energy Models (REM) with logarithmically correlated random potential, above and at the glass transition temperature. The random potential sequences…
The paper deals with homogenization of self-adjoint operators in $L_2(\mathbb R^d)$ of the form $$ ({\mathbb A}_\eps u) (\x) = \int_{\R^d} \mu(\x/\eps, \y/\eps) \frac{\left( u(\x) - u(\y) \right)}{|\x - \y|^{d+\alpha}}\,d\y, $$ where $0<…
We adress the problem of Laplace deconvolution with random noise in a regression framework. The time set is not considered to be fixed, but grows with the number of observation points. Moreover, the convolution kernel is unknown, and…
In this article new bounds on weighted p-norms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl--Heisenberg signaling in…
We study a commonly-used second-kind boundary-integral equation for solving the Helmholtz exterior Neumann problem at high frequency, where, writing $\Gamma$ for the boundary of the obstacle, the relevant integral operators map…
This paper proposes and studies new quantum version of $f$-divergences, a class of convex functionals of a pair of probability distributions including Kullback-Leibler divergence, Rnyi-type relative entropy and so on. There are several…
We consider the problem of estimating an RF-device's location based on observations, such as received signal strength, from a set of transmitters with known locations. We survey the literature on this problem, showing that previous authors…