Generalized eigenfunctions of the two-dimensional relativistic Schrödinger operator H = √ −∆ + V (x) with |V (x)| ≤ C〈x〉−σ, σ > 3/2, are considered. We compute the integral kernels of the boundary values R± 0 (λ) = ( √ −∆− (λ± i0))−1, and prove that the generalized eigenfunctions φ±(x, k) are bounded on R x × {k | a ≤ |k| ≤ b}, where [a, b] ⊂ (0,∞)\σp(H), and σp(H) is the set of eigenvalues of ...

This paper addresses the problem of using the Karhunen-Lo eve transform with partial data. Given a set of empirical eigenfunctions we show how to recover the modal coeecients for each gappy snapshot by a least-squares procedure. This method gives an unbiased estimate of the data that lay in the gaps and permits gaps to be lled in a reasonable manner. In addition, a scheme is advanced for nding ...

A general program to show quantum-classical correspondence for bound conservative integrable and chaotic systems is described. The method is applied to integrable systems and the nature of the approach to the classical limit, the cancellation of essential singularities, is demonstrated. The application to chaotic systems requires an understanding of classical Liouville eigenfunctions and a Liou...

The basic boundary-contact oscillation problems are considered for a three-dimensional piecewise-homogeneous isotropic elastic medium bounded by several closed surfaces. Using Carleman’s method, the asymptotic formulas for the distribution of eigenfunctions and eigenvalues are obtained. 1. After the remarkable papers of T. Carleman [1–2] the method based on the asymptotic investigation of the r...

We consider a basic d-adic model for the scattering transform on the line. We prove L bounds for this scattering transform and a weak L bound for a Carleson type maximal operator (Theorem 1.4). The latter implies boundedness of d-adic models of generalized eigenfunctions of Dirac type operators with potential in L(IR). We show that this result cannot be obtained by estimating the terms in the n...

Basing on the constraint equalities which arise from the algebra of the collinear conformal group and the conformal operator product expansion, we predict the solutions of the leading order evolution equations for the non-forward distributions, including transversity, in terms of the conformal moments; next-to-leading order flavour singlet coefficient functions for the polarized and unpolarized...

The exploitation of natural symmetries (mirror images) in a well-defined family of patterns (human faces) is discussed within the framework of the Karhunen-Lo&e expansion. This results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix, without increasing the complexity of the calculation. The resulting approximation of faces projected f...

The exploitation of natural symmetries (mirror images) in a well-defined family of patterns (human faces) is discussed within the framework of the Karhunen-L&ve expansion. This results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix, without increasing the complexity of the calculation. The resulting approximation of faces projected f...

Basing on the constraint equalities which arise from the algebra of the collinear conformal group and the conformal operator product expansion, we predict the solutions of the leading order evolution equations for the non-forward distributions, including transversity, in terms of the conformal moments; next-to-leading order flavour singlet coefficient functions for the polarized and unpolarized...

This article presents a methodology for the synthesis of finite-dimensional nonlinear output feedback controllers for nonlinear parabolic partial differential equation (PDE) systems with time-dependent spatial domains. Initially, the nonlinear parabolic PDE system is expressed with respect to an appropriate time-invariant spatial coordinate, and a representative (with respect to different initi...