The aim of this paper is to construct a generalized Fourier analysis for certain Hermitian operators. When A, B are entire functions, then H(A,B) will be the associated reproducing kernel Hilbert spaces of Cn×n-valued functions. In that case, we will construct the expansion theorem forH(A,B) in a comprehensive manner. The spectral functions for the reproducing kernel Hilbert spaces will also be...

Bourgain [Bou02] showed that any noise stable Boolean function f can be well-approximated by a junta. In this note we give an exponential sharpening of the parameters of Bourgain’s result under the additional assumption that f is a halfspace.

We have developed an experimental platform that allows a large number of human participants to interact in real-time within a common virtual world. Within this environment, human participants foraged for resources distributed in two pools. In addition to varying the relative replenishment rates for the two resources (50-50, 65-35, 80-20), we manipulated whether participants could see each other...

and Applied Analysis 3 2. Main Result We first give some definitions 12 . Definition 1. A function f : R → R is called real analytic quasi-periodic with frequencies μ1, . . . , μm if it can be represented as a Fourier series of the type

Chvátal’s conjecture in extremal combinatorics asserts that for any decreasing family F of subsets of a finite set S, there is a largest intersecting subfamily of F consisting of all members of F that include a particular x ∈ S. In this paper we reformulate the conjecture in terms of influences of variables on Boolean functions and correlation inequalities, and study special cases and variants ...

x2 + y2. Note that |z| is the distance of z from 0. Also note that |z|2 = zz. The complex exponential function e is defined to be equal to cos(θ)+ i sin(θ). Note that e is a point on the unit circle, x + y = 1. Any complex number z can be written in the form re where r = |z| and θ is an appropriately chosen angle; this is sometimes called the polar form of the complex number. Considered as a fu...

We propose a general framework for Fourier analysis in the eld of genetic algorithms. We introduce special functions, analogous to sine and cosine for real numbers, that have nice properties with respect to genetic operations such as mutation and crossover. The special functions we introduce are generalizations of bit products and Walsh products. As applications, we trace (both analytically and...