In this paper, we investigate a posteriori error estimates of the Galerkin spectral methods for
second-order equations, and propose a simple type of error estimator comprising expansion …

In this paper we provide a new linear sampling method based on the same data but a
different definition of the data operator for two inverse problems: the multi-frequency inverse …

In this work we connect machine learning techniques, in particular kernel machine learning,
to inverse source and scattering problems. We show the proposed kernel machine learning …

We consider the inverse medium scattering of reconstructing the medium contrast using
Born data, including the full-aperture, limited-aperture, and multifrequency data. We propose …

In 1961 [60], the prolate spheroidal wave functions (PSWFs) were shown to be the
eigenfunctions of the finite Fourier transformations. In that paper, also, some properties of …

In this paper, we present an hp analysis of the mortar spectral element method for the
Schrödinger eigenvalue problem (− Δ+ c 2‖ x‖ 2) u= λ u, and thereby justify the numerical …

Prolate spheroidal wave functions have long been used in mathematical physics as a basis
in which to expand solutions of the Helmholtz equation in prolate spheroidal coordinates …

In this paper, we introduce a new family of orthogonal systems, termed as the Müntz ball
polynomials (MBPs), which are orthogonal with respect to the weight function:‖ x‖ 2 θ+ 2 μ …

We investigate the construction of multidimensional prolate spheroidal wave functions using
techniques from Clifford analysis. The prolates are defined to be eigenfunctions of a certain …

An efficient spectral-Galerkin method for eigenvalue problems of the integral fractional
Laplacian on a unit ball of any dimension is proposed in this paper. The symmetric positive …