Related papers: Certain inequalities involving prolate spheroidal …
One of the fundamental problems in communications is finding the energy distribution of signals in time and frequency domains. It should, therefore, be of great interest to find the most energy concentration hypercomplex signal. The present…
We derive a spectral representation for the oblate spheroidal wave operator which is holomorphic in the aspherical parameter $\Omega$ in a neighborhood of the real line. For real $\Omega$, estimates are derived for all eigenvalue gaps…
Imaging with a layered superlens is a spatial filtering operation characterized by the point spread function (PSF). We show that in the same optical system the image of a narrow sub-wavelength Gaussian incident field may be surprisingly…
This paper is a continuation of our previous works about coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It concerns a study on the properties of wavefunctions in the phase space…
Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more…
The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used to study the spheroidal wave functions' recurrence relations, which are revealed by the shape-invariance property of the super-potential. The super-potential is…
This paper presents some new results on the eigenvalues of the spheroidal wave equation. We study the angular and Coulomb spheroidal wave equation as a special case of a more general linear Hamiltonian system depending on three parameters.…
In addition to being the eigenfunctions of the restricted Fourier operator, the angular spheroidal wave functions of the first kind of order zero and nonnegative integer characteristic exponents are the solutions of a singular self-adjoint…
A previous article showed that alternative expressions for calculating oblate spheroidal radial functions of both kinds can provide accurate values over very large parameter ranges using double precision arithmetic, even where the…
In this paper, we use the means of super-symmetric quantum mechanics to study of the Spin-weighted Spheroidal Wave in the case of s=3/2. We obtain some interesting results: the first-five terms of the super-potential, the general form of…
In this paper we show that the classical problem of frequency estimation can be formulated and solved efficiently in an empirical Bayesian framework by assigning a uniform a priori probability distribution to the unknown frequency. We…
In this paper, we first give two uniform asymptotic approximations of the eigenfunctions of the weighted finite Fourier transform operator, defined by ${\displaystyle \mathcal F_c^{(\alpha)} f(x)=\int_{-1}^1 e^{icxy}…
Surface plasma waves (SPWs) have been extensively studied in the past two decades with a promise for many applications. However, the effort has so far been met with limited success. It is widely believed that a major caveat lies with the…
A new set of vector solutions to Maxwell's equations based on solutions to the wave equation in spheroidal coordinates allows laser beams to be described beyond the paraxial approximation. Using these solutions allows us to calculate the…
Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…
Pseudodifferential parabolic equations with an operator square root arise in wave propagation problems as a one-way counterpart of the Helmholtz equation. The expression under the square root usually involves a differential operator and a…
In this paper we study the eigenvalues of the angular spheroidal wave equation and its generalization, the Coulomb spheroidal wave equation. An associated differential system and a formula for the connection coefficients between the various…
The spin-weighted spheroidal eigenvalues and eigenfunctions arise in the separation by variables of spin-field perturbations of Kerr black holes. We derive a large, real-frequency asymptotic expansion of the spin-weighted spheroidal…
We investigate the application of windowed Fourier frames (WFFs) to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is…
Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and concerned concrete special…