No: 2207 Authors: Seongho Seo, Moo K. Chung, Kim M. Dalton, Richard J. Davidson Institutions: Seoul National University, Seoul, Korea University of Wisconsin, Madison, WI, USA Introduction: A shape representation is an important problem to understand brain morphological changes related to illness or disease. We represent a new shape representation method using the eigenfunctions of Laplace-Belt...

We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator. Given the set of call and put dates, the callable and putable bond pricing function is the value function...

Critical Dirac operators are those which have eigenfunctions and/or resonances for E = m. We estimate the behavior of the generalized eigenfunctions of critical Dirac operators under small perturbations of the potential. The estimates are done in the L∞-norm. We show that for small k the generalized eigenfunctions are in leading order multiples of the respective eigenfunctions and/or resonances...

An atomic decomposition is considered in Banach space.  A method for constructing an atomic decomposition of Banach  space, starting with atomic decomposition of  subspaces  is presented. Some relations between them are established. The proposed method is used in the  study  of the  frame  properties of systems of eigenfunctions and associated functions of discontinuous differential operators.

In this paper we shall consider the new projection scheme of streaming waveform data processing for text-independent speaker indexing from continuous speech. It is based on an expansion into series of eigenfunctions of the Fourier transform. Partly this scheme can be also used for speech recognition.

We analyze the 2D magnetic Laplacian in the semiclassical limit in the case when the magnetic field vanishes along a smooth curve. In particular, we prove local and microlocal estimates for the eigenfunctions and a complete asymptotic expansion of the eigenpairs in powers of h.

We propose a newmethod to analyze and represent data recorded on a domain of general shape in R by computing the eigenfunctions of Laplacian defined over there and expanding the data into these eigenfunctions. Instead of directly solving the eigenvalue problemon such a domain via theHelmholtz equation (which can be quite complicated and costly), we find the integral operator commuting with the ...

In this paper, we analyze the eigenfunctions of the edge-based Laplacian on a graph and the relationship of these functions to random walks on the graph. We commence by discussing the set of eigenfunctions supported at the vertices, and demonstrate the relationship of these eigenfunctions to the classical random walk on the graph. Then, from an analysis of functions supported only on the interi...