The linearized Vlasov equation for a plasma system in a uniform magnetic field and the corresponding linear Vlasov operator are studied. The spectrum and the corresponding eigenfunctions of the Vlasov operator are found. The spectrum of this operator consists of two parts: one is continuous and real; the other is discrete and complex. Interestingly, the real eigenvalues are infinitely degenerat...

We present a computational method for solving a class of boundary-value problems in Sturm-Liouville form. The algorithms are based on global polynomial collocation methods and produce discrete representations of the eigenfunctions. Error control is performed by evaluating the eigenvalue problem residuals generated when the eigenfunctions are interpolated to a finer discretization grid; eigenfun...

A semi-analytical technique to simulate spatially dispersive (SD) cylindrical metasurfaces is proposed and demonstrated. This method based on the well-known Eigenfunction Expansion (EFE) extends work of [1],[2] by integrating Extended GSTCs into this pre-existing specific surfaces. then applied several composed wire dipole unit cells, successfully verified against commercial full-wave simulatio...

The Askey-Wilson function transform is a q-analogue of the Jacobi function transform with kernel given by an explicit non-polynomial eigenfunction of the Askey-Wilson second order q-difference operator. The kernel is called the Askey-Wilson function. In this paper an explicit expansion formula for the Askey-Wilson function in terms of Askey-Wilson polynomials is proven. With this expansion form...

This paper is devoted to the derivation of expansion and sampling theorems associated with nth order discontinuous eigenvalue problems defined on [−1, 1], illustrated with detailed examples. The problem consists of nth order differential expressions and n boundary and n compatibility conditions at x = 0. The differential expressions are defined, in general, in two different ways throughout [−1,...