Related papers: New method of bandlimited extrapolation

This paper concerns linear first-order hyperbolic systems in one space dimension of the type $$ \partial_tu_j + a_j(x,t)\partial_xu_j + \sum\limits_{k=1}^nb_{jk}(x,t)u_k = f_j(x,t),\; x \in (0,1),\; j=1,\ldots,n, $$ with periodicity…

We consider drift parameter estimation in a model driven by the sum of two independent fractional Brownian motions with different Hurst indices. Although the maximum likelihood estimator (MLE) for this model is known theoretically, its…

This paper deals with an inertial proximal algorithm that contains a Tikhonov regularization term, in connection to the minimization problem of a convex lower semicontinuous function $f$. We show that for appropriate Tikhonov regularization…

In this paper we establish the existence of at least two weak solutions for the following fractional Kirchhoff problem involving singular and exponential nonlinearity \begin{equation*} \left\{\begin{split}…

In this paper, we take the first step towards an extension of the nonlinear steepest descent method of Deift, Its and Zhou to the case of operator Riemann-Hilbert problems. In particular, we provide long range asymptotics for a Fredholm…

A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…

In this paper we study the existence of solutions to the following generalized nonlinear two-parameter problem \begin{equation*} a(u, v) \; =\; \lambda\, b(u, m) + \mu\, m(u, v) + \varepsilon\, F(u, v), \end{equation*} for a triple $(a, b,…

A numerical algorithm to decompose an exact low-rank skew-symmetric tensor into a sum of elementary (rank-$1$) skew-symmetric tensors is introduced. The algorithm uncovers this Grassmann decomposition based on linear relations that are…

In this paper we address the problem of estimating the ratio $\frac{q}{p}$ where $p$ is a density function and $q$ is another density, or, more generally an arbitrary function. Knowing or approximating this ratio is needed in various…

We extend the classical trace (and determinant) known for the integral operators $$ ({\mathcal I}+)\int_{[0,1)^N}{\bf A}({\bf k},{\bf x}){\bf u}({\bf x})d{\bf x} $$ with matrix-valued kernels ${\bf A}$ to the operators of the form $$…

We examine convergent representations for the sum of a decaying exponential and a Bessel function in the form \[\sum_{n=1}^\infty \frac{e^{-an}}{(\frac{1}{2} bn)^\nu}\,J_\nu(bn),\] where $J_\nu(x)$ is the Bessel function of the first kind…

In this work we analyze the complex scaling method applied to the problem of time-harmonic scalar wave propagation in junctions between `leaky,' or open dielectric waveguides. In [arXiv:2302.04353, arXiv:2310.05816, arXiv:2401.04674,…

In this paper, we consider the deformed Fredholm determinant of the confluent hypergeometric kernel. This determinant represents the gap probability of the corresponding determinantal point process where each particle is removed…

We reexamine and extend a group of solutions in series of Bessel functions for a limiting case of the confluent Heun equation and, then, apply such solutions to the one-dimensional Schr\"odinger equation with an inverted quasi-exactly…

We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…

The level spacing distributions which arise when one rescales the Laguerre or Jacobi ensembles of hermitian matrices is studied. These distributions are expressible in terms of a Fredholm determinant of an integral operator whose kernel is…

The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…

A semilinear parabolic problem of second order with an unknown time-convolution kernel is considered. The missing kernel is recovered from an additional integral measurement. The existence, uniqueness and regularity of a weak solution is…

In this paper, we develop a new scaling method to study spectral and Bergman kernels for the k-th tensor power of a line bundle over a complex manifold under local spectral gap condition. In particular, we establish a simple proof of the…

We adress the problem of spherical deconvolution in a non parametric statistical framework, where both the signal and the operator kernel are subject to error measurements. After a preliminary treatment of the kernel, we apply a…