The Schwartz algebra of an affine Hecke algebra

For a general affine Hecke algebra H we study its Schwartz completion S. The main theorem is an exact description of the image of S under the Fourier isomorphism. An important ingredient in the proof of this result is the definition and computation of the constant terms of a coefficient of a generalized principal series representation. Finally we discuss some consequences of the main theorem for the theory of tempered representations of H

A two-axis laser boresight system for a shuttle experiment

A two-axis gimballed laser pointing mechanism is being developed for the Lidar In-space Technology Experiment (LITE) to be flown on the National Space Transportation System (NSTS) Space Shuttle in February 1993. This report describes the design requirements and goals, the configuration, analysis, and testing plans for this laser pointing device

The Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory

Fractional Brownian motion is a non-Markovian Gaussian process $X_t$, indexed by the Hurst exponent $H$. It generalises standard Brownian motion (corresponding to $H=1/2$). We study the probability distribution of the maximum $m$ of the process and the time $t_{\rm max}$ at which the maximum is reached. They are encoded in a path integral, which we evaluate perturbatively around a Brownian, setting $H=1/2 + \varepsilon$. This allows us to derive analytic results beyond the scaling exponents. Extensive numerical simulations for different values of $H$ test these analytical predictions and show excellent agreement, even for large $\varepsilon$.Comment: 5 pages, 7 figure

Continuants and some decompositions into squares

In 1855 H. J. S. Smith proved Fermat's two-square using the notion of palindromic continuants. In his paper, Smith constructed a proper representation of a prime number $p$ as a sum of two squares, given a solution of $z^2+1\equiv0\pmod{p}$, and vice versa. In this paper, we extend the use of continuants to proper representations by sums of two squares in rings of polynomials on fields of characteristic different from 2. New deterministic algorithms for finding the corresponding proper representations are presented. Our approach will provide a new constructive proof of the four-square theorem and new proofs for other representations of integers by quaternary quadratic forms.Comment: 21 page