Fourier Analysis on GL(n,R)

The GlnR Regulon in Streptococcus mutans Is Differentially Regulated by GlnR and PmrA

GlnR-mediated repression of the GlnR regulon at acidic pH is required for optimal acid tolerance in Streptococcus mutans, the etiologic agent for dental caries. Unlike most streptococci, the GlnR regulon is also regulated by newly identified PmrA (SMUGS5_RS05810) at the transcriptional level in S. mutans GS5. Results from gel mobility shift assays confirmed that both GlnR and PmrA recognized th...

Isogeometric analysis: vibration analysis, Fourier and wavelet spectra

This paper presents the Fourier and wavelet characterization of vibratio...

Fourier Analysis

(1.1) |〈u,v〉| ≤ ‖u‖ ‖v‖. An outline of a proof of this fundamental inequality, when V = R and ‖ · ‖ is the standard Eucledian norm, is given in Exercise 24 of Section 2.7 of [1]. We will give a proof in the general case at the end of this section. LetW be an n dimensional subspace of V and let P : V 7→W be the corresponding projection operator, i.e. if v ∈ V then w = Pv ∈W is the element in W w...

Fourier Analysis

Montréal Notes on Quadratic Fourier Analysis

These are notes to accompany four lectures that I gave at the School on additive combinatorics, held in Montréal, Québec between March 30th and April 5th 2006. My aim is to introduce “quadratic fourier analysis” in so far as we understand it at the present time. Specifically, we will describe “quadratic objects” of various types and their relation to additive structures, particularly four-term ...