A sufficient condition for the boundedness of operator-weighted martingale transforms and Hilbert transform

Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space H. We show that if W and its inverse W−1 both satisfy a matrix reverse Holder property introduced in [2], then the weighted Hilbert transform H : L2W(R,H) → L2W(R,H) and also all weighted dyadic martingale transforms Tσ: L2W(R,H) → L2W(R,H) are bounded. We also show that this condition is not necessary for the boundedness of the weighted Hilbert transform

Using electronic structure changes to map the H-T phase diagram of alpha'-NaV2O5

We report polarized optical reflectance studies of \alpha'-NaV2O5 as a function of temperature (4-45 K) and magnetic field (0-60 T). Rung directed electronic structure changes, as measured by near-infrared reflectance ratios \Delta R(H)=R(H)/R(H=0 T), are especially sensitive to the phase boundaries. We employ these changes to map out an H-T phase diagram. Topological highlights include the observation of two phase boundaries slightly below T_{SG}, enhanced curvature of the 34 K phase boundary above 35 T, and, surprisingly, strong hysteresis effects of both transitions with applied field.Comment: 4 pages, 3 figures, PRB accepte

The semiquinone radical anion of 1,10-phenanthroline-5,6-dione: synthesis and rare earth coordination chemistry

Reduction of 1,10-phenanthroline-5,6-dione (pd) with CoCpR2 resulted in the first molecular compounds of the pd˙− semi-quinone radical anion, [CoCpR2]+[pd]˙− (R = H, (1); R = Me4, (2)). Furthermore compounds 1 and 2 were reacted with [Y(hfac)3(thf)2] (hfac = 1,1,1-5,5,5-hexafluoroacetylacetonate) to synthesise the rare earth-transition metal heterometallic compounds, [CoCpR2]+[Y(hfac)3(N,N′-pd)]˙− (R = H, (3); R = Me4, (4))

Harmonic Analysis of Signed Ruelle Transfer Operators

Motivated by wavelet analysis, we prove that there is a one-to-one correspondence between the following data: Solutions to $R(h)=h$ where $R$ is a certain non-positive Ruelle transfer operator; Operators that intertwine a certain class of representations of the $C^*$-algebra $\mathfrak{A}_N$ on two unitary generators $U$, $V$ subject to the relation $$UVU^{-1}=V^N$$ This correspondence enables us to give a criterion for the biorthogonality of a pair of scaling functions and calculate all solutions of the equation $R(h)=h$ in some concrete cases.Comment: 24 page