Related papers: Vectorial ball Prolate spheroidal wave functions w…
The problem of a fermion subject to a general mixing of vector and scalar potentials in a two-dimensional world is mapped into a Sturm-Liouville problem. Isolated bounded solutions are also searched. For the specific case of an inversely…
This study applies the RBF wavelet series to the evaluation of analytical solutions of linear time-dependent wave and diffusion problems of any dimensionality and geometry. To the best of the author's knowledge, such analytical solutions…
We study the asymptotic behaviour of eigenvalues and eigenfunctions of a boundary value problem for the Sturm-Liouville operator with general boundary conditions and the weight function perturbed by the so-called $\delta'$-like sequence…
In arXiv:1306.2914 a method for approximate solution of Sturm-Liouville equations and related spectral problems was presented based on the construction of the Delsarte transmutation operators. The problem of numerical approximation of…
We describe a method for the numerical evaluation of the angular prolate spheroidal wave functions of the first kind of order zero. It is based on the observation that underlies the WKB method, namely that many second order differential…
A central result of Sturm-Liouville theory (also called the Sturm-Hurwitz Theorem) states that if $\phi_k$ is a sequence of eigenfunctions of a second order differential operator on the interval $I \subset \mathbb{R}$, then any linear…
To obtain a local description from highly accurate density functional theory codes that are based on modified plane wave bases, a transformation to a local orthonormal Wannier function basis is required. In order to do so while enforcing…
We examine the spectrum of a family of Sturm--Liouville operators with regularly spaced delta function potentials parametrized by increasing strength. The limiting behavior of the eigenvalues under this spectral flow was described in a…
Our main objective in this work is to show how Sobolev orthogonal polynomials emerge as a useful tool within the framework of spectral methods for boundary-value problems. The solution of a boundary-value problem for a stationary…
We study linear PDE constraints for vector-valued functions and distributions. Our focus lies on wave solutions. These give rise to distributions with low-dimensional support. Special waves from vector potentials are represented by…
We establish inversion formulas of the so called filtered back-projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball. We also find several…
Accurately estimating the point spread function (PSF) of an optical system requires solving free-space wave propagation, which entails evaluating a diffraction integral. This integral is traditionally computed numerically using Fast Fourier…
We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre…
The Fourier transform truncated on [-c,c] is usually analyzed when acting on L^2(-1/b,1/b) and its right-singular vectors are the prolate spheroidal wave functions. This paper considers the operator acting on the larger space L^2(exp(b|.|))…
We consider a Sturm--Liouville boundary value problem in a boun\-ded domain $\cD$ of $\mathbb{R}^n$. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in $\cD$ and the boundary…
The problem of a fermion subject to a convenient mixing of vector and scalar potentials in a two-dimensional space-time is mapped into a Sturm-Liouville problem. For a specific case which gives rise to an exactly solvable effective modified…
Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher…
Divergence-free (div-free) and curl-free vector fields are pervasive in many areas of science and engineering, from fluid dynamics to electromagnetism. A common problem that arises in applications is that of constructing smooth approximants…
We consider the inverse medium scattering of reconstructing the medium contrast using Born data, including the full aperture, limited-aperture, and multi-frequency data. We propose data-driven basis functions for these inverse problems…
In this study, we define discrete fractional Sturm-Liouville (DFSL) operators within Riemann-Liouville and Gr\"unwald-Letnikov fractional operators with both delta and nabla operators. We show selfadjointness of the DFSL operator for the…