Two theorems on finite Hilbert transforms

Two-dimensional Hilbert Transforms'

Sato-tate Theorems for Mellin Transforms over Finite Fields

as χ varies over all multiplicative characters of k. For each χ, S(χ) is real, and (by Weil) has absolute value at most 2. Evans found empirically that, for large q = #k, these q − 1 sums were approximately equidistributed for the “Sato-Tate measure” (1/2π) √ 4− x2dx on the closed interval [−2, 2], and asked if this equidistribution was provably true. Rudnick had done numerics on the sums T (χ)...

Sato-tate Theorems for Finite-field Mellin Transforms

as χ varies over all multiplicative characters of k. For each χ, S(χ) is real, and (by Weil) has absolute value at most 2. Evans found empirically that, for large q = #k, these q − 1 sums were approximately equidistributed for the “Sato-Tate measure” (1/2π) √ 4− x2dx on the closed interval [−2, 2], and asked if this equidistribution was provably true. Rudnick had done numerics on the sums T (χ)...

Classical Wavelet Transforms over Finite Fields

This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...

Two Embedding Theorems for Finite Lattices

Introduction. One of the important unsolved problems of lattice theory is the problem of embedding every finite lattice in a finite partition lattice. The partition lattice can be considered as the lattice of subspaces of a suitable geometry. By slightly loosening the conditions on this geometry it will be shown that every finite lattice can be embedded in the lattice of subspaces of a finite g...