Evolvability via the Fourier transform

Fast Approximate Fourier Transform via Wavelets Transform

We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. If no intermediate coeecients are dropped and no approximations are made, the proposed algorithm computes the exact result, and its computational comple...

Learning Boolean Functions via the Fourier Transform

We survey learning algorithms that are based on the Fourier Transform representa tion In many cases we simplify the original proofs and integrate the proofs of related results We hope that this would give the reader a complete and comprehensive un derstanding of both the results and the techniques Introduction The importance of using the right representation of a function in order to approximat...

12 Invariant Nonlinear Correlations via Fourier Transform

Multicomplementary operators via finite Fourier transform

Abstract. A complete set of d + 1 mutually unbiased bases exists in a Hilbert spaces of dimension d, whenever d is a power of a prime. We discuss a simple construction of d+1 disjoint classes (each one having d−1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construc...

Torelli Theorem via Fourier - Mukai Transform

We show that the Fourier transform on the Jacobian of a curve interchanges " δ functions " on the curve and the theta divisor. The Torelli theorem is an immediate consequence. 1. Statement of the theorem. 1.1. We live over an algebraically closed base field k. Let J be an abelian variety equipped with a principal polarization θ : J ∼ → J • = Pic 0 (J), so we have the corresponding Fourier trans...