Abstract: In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at p locations with n repeated measurements. While principal component analysis (PCA) is commonly applied to find the patterns, the eigenimages produced from PCA may be noisy or exhibit patterns that are not physically meaningful when p is large relative ...

T he knowledge of the eigenfunctions of a linear time-varying (LTV) system is a fundamental issue from both theoretical and applications points of view. Nonetheless, no analytic expressions are available for the eigenfunctions of a general LTV system. However, approximate expressions have been proposed for slowly-varying operators. In particular, in [1] it was shown that an underspread system c...

In [1] and [2], Bernstein and Reznikov have introduced a new way of estimating the coefficients in the spectral expansion of φ2, where φ is a Maass cusp of norm 1 on a quotient Y = Γ\H of the Poincaré upper half-plane with finite volume. The question of obtaining the precise exponential decay of those coefficients had been posed by Selberg, and first solved by Good [5] (for holomorphic forms) a...

The large distance behavior of weakly bound three-body systems is investigated. The Schr odinger equation and the Faddeev equations are reformulated by an expansion in eigenfunctions of the angular part of a corresponding operator. The resulting coupled set of e ective radial equations are then derived. Both twoand three-body asymptotic behavior are possible and their relative importance is st...

We consider the Laplace operator with Dirichlet boundary conditions on a domain in R and study the effect that performing a scaling in one direction has on the eigenvalues and corresponding eigenfunctions as a function of the scaling parameter around zero. This generalizes our previous results in two dimensions and, as in that case, allows us to obtain an approximation for Dirichlet eigenvalues...

we investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. a self-adjoint linear operator a is defined in a suitable hilbert space h such that the eigenvalues of such a problem coincide with those of a . we discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. finally, we obtain th...