‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

We introduce eigenfunctions of the Reed-Muller transform. Eigenfunctions are functions whose canonical sumof-products expression and PPRM (positive polarity ReedMuller expression) are isomorphic. In the case of symmetric functions, the eigenfunction can be viewed as a function whose reduced truth vector is identical to the reduced ReedMuller spectrum. We show that the number of symmetric (ordin...

The linearized Vlasov equation for a plasma system in an external constant magnetic field and the corresponding linear Vlasov operator are studied. The solution of the Vlasov equation is found by the resolvent method. The spectrum and eigenfunctions of the Vlasov operator are also found. The spectrum of this operator consists of two parts: one is continuous and real; the other is discrete and c...

These lectures are devoted to nodal geometry of eigenfunctions φλ of the Laplacian ∆g of a Riemannian manifold (M, g) of dimension m and to the associated problems on L norms of eigenfunctions. The manifolds are generally assumed to be compact, although the problems can also be posed on non-compact complete Riemannian manifolds. The emphasis of these lectures is on real analytic Riemannian mani...

We study eigenstates of chaotic billiards in the momentum representation and propose the radially integrated momentum distribution as useful measure to detect localization effects. For the momentum distribution, the radially integrated momentum distribution, and the angular integrated momentum distribution explicit formulae in terms of the normal derivative along the billiard boundary are deriv...

We review the properties of eigenvalues and eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundary condition. We keep the presentation at a level accessible to scientists from various disciplines ranging from mathematics to physics and computer sciences. The main focus is put onto multiple intricate relations between the shape of a domain a...