This paper introduces the technique of Fourier analysis applied to Boolean functions. We use this technique to illustrate proofs of both Arrow’s Impossibility Theorem and H̊astad’s 3-bit Theorem.

We discuss some of the ideas behind the study of upper bound questions in classical discrepancy theory. The many ideas involved come from diverse areas of mathematics and include diophantine approximation, probability theory, number theory and various forms of Fourier analysis. We illustrate these ideas by largely restricting our discussion to two dimensions.

Hart, Iosevich, Koh and Rudnev (2007) show, using Fourier analysis method, that the finite Erdös-Falconer distance conjecture holds for subsets of the unit sphere in Fdq . In this note, we give a graph theoretic proof of this result.

practical fourier analysis for multigrid methods. Book lovers, when you need a new book to read, find the book here. Never worry not to find what you need. Is the practical fourier analysis for multigrid methods your needed book now? That's true; you are really a good reader. This is a perfect book that comes from great author to share with you. The book offers the best experience and lesson to...

We overview and discuss several methods for the Fourier analysis of symbolic data, such as DNA sequences, emphasizing their mutual connections. We consider the indicator sequence approach, the vector and the symbolic autocorrelation methods, and methods such as the spectral envelope, that for each frequency optimize the symbolic-no-numeric mapping to emphasize any periodic data features. We dis...

Identifying PSL(2,C) as a projective group for patterns in the conformal camera model, the projective harmonic analysis on its double covering group SL(2,C) is presented in the noncompact and compact pictures–the pictures used to study different aspects of irreducible unitary representations of semisimple Lie groups. Bypassing technicalities of representation theory, but stressing the motivatio...

In this paper, we develop some important Fourier analysis tools in the context of time scales. In particular, we present a generalized Fourier transform in this context as well as a critical inversion result. This leads directly to a convolution for signals on two (possibly distinct) time scales as well as several natural classes of time scales which arise in this setting: dilated, closed under...

Hitherto communication theory was based on two alternative methods of signal analysis. One is the description of the signal as a function of time; the other is Fourier analysis. Both are idealizations, as the first method operates with sharply defined instants of time, the second with infinite wave-trains of rigorously defined frequencies. But our everyday experiences—especially our auditory se...

This work is supported by National Nature Science Foundation of China (69982005) and Projects of Development Plan of the State Key Foundation Search (G199803050703) Abstract: A robust approach is proposed for document skew detection. We use Fourier analysis and SVM to classify textual areas from non-textual areas of documents. We also propose a robust method to determine the skew angle from tex...