Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Kn...

This paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture α and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular, for any orientation of the magnetic field, we prove the existence of discrete spectrum below the essential spectrum in the limit α → 0 and establish a full asymptotic...

A framework is presented for step-by-step implementation of weighted-residual methods (MWR) for simulations that require the solution of boundary-value problems. A set of Matlab-based functions of the computationally common MWR solution steps has been developed and is used in the application of eigenfunction expansion, collocation, and Galerkin-projection discretizations of time-dependent, dist...

In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold X. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on X. This extends the result for analytic functions on compact manifold by Seeley [See69], and the characterisation of Gevrey functions and Gevrey u...

This paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture α and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular, for any orientation of the magnetic field, we prove the existence of discrete spectrum below the essential spectrum in the limit α → 0 and establish a full asymptotic...

In this work, we prove the existence of a spectral function for singular q-Sturm-Liouville operator. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.

We prove that for the uniquely ergodic R action associated with a primitive substitution tiling of finite local complexity, every measurable eigenfunction coincides with a continuous function almost everywhere. Thus, topological weak-mixing is equivalent to measure-theoretic weak-mixing for such actions. If the expansion map for the substitution is a pure dilation by θ > 1 and the substitution ...

Using tools from semiclassical analysis, we give weighted L∞ estimates for eigenfunctions of strictly convex surfaces of revolution. These estimates give rise to new sampling techniques and provide improved bounds on the number of samples necessary for recovering sparse eigenfunction expansions on surfaces of revolution. On the sphere, our estimates imply that any function having an s-sparse ex...

Directional emission from a slit surrounded by rectangular grooves on the exit surface in a conducting plane is investigated. An electromagnetic boundaryvalue problem dealing with a slit surrounded by rectangular grooves on the exit surface in a conducting plane is rigourously solved based on the Fourier transform, eigenfunction expansion, and mode-matching method. The radiation pattern from th...