NONPARAMETRIC IDENTIFICATION OF POSITIVE EIGENFUNCTIONS

Positive Eigenfunctions of a Schrödinger Operator

The paper considers the eigenvalue problem −∆u − αu + λg(x)u = 0 with u ∈ H(R ), u = 0, where α, λ ∈ R and g(x) ≡ 0 on Ω, g(x) ∈ (0, 1] on R \ Ω and lim |x |→+∞ g(x) = 1 for some bounded open set Ω ∈ RN . Given α > 0, does there exist a value of λ > 0 for which the problem has a positive solution? It is shown that this occurs if and only if α lies in a certain interval (Γ, ξ1) and that in this ...

Nonparametric System Identification

This article presents a survey of various methods for nonparametric identification of nonlinear systems. Nonparametric identification methods are those that measure Wiener kernels or Volterra kernels, since an output of a nonlinear system can be described by the convolution integral of Wiener or Volterra kernels and the system input. Section 1 highlights the representation methods of nonlinear ...

Positive eigenfunctions of the Laplacian andconformal densities on homogeneous trees

In this paper, we study some asymptotic aspects of the positive eigenfunctions of the combinatorial Laplacian associated to a homogeneous tree. The results are inspired by results of Dennis Sullivan concerning ?harmonic functions on the hyperbolic spaces H I n and contained in the paper Sul]. Let k be an integer 3 and X the homogeneous tree of degree k, that is, the unique simply connected simp...

Nonparametric Identification of Copula Structures

We propose a unified framework for testing a variety of assumptions commonly made about the structure of copulas, including symmetry, radial symmetry, joint symmetry, associativity and Archimedeanity, and max-stability. Our test is nonparametric and based on the asymptotic distribution of the empirical copula process. We perform simulation experiments to evaluate our test and conclude that our ...

NONPARAMETRIC IDENTIFICATION Rosa