On the Convergence of Lacunary Walsh-Fourier Series

We study the Walsh-Fourier series of S_{n_j}f, along a lacunary subsequence of integers {n_j}. Under a suitable integrability condition, we show that the sequence converges to f a.e. Integral condition is only slightly larger than what the sharp integrability condition would be, by a result of Konyagin. The condition is: f is in L loglog L (logloglog L). The method of proof uses four ingredients, (1) analysis on the Walsh Phase Plane, (2) the new multi-frequency Calderon-Zygmund Decomposition of Nazarov-Oberlin-Thiele, (3) a classical inequality of Zygmund, giving an improvement in the Hausdorff-Young inequality for lacunary subsequences of integers, and (4) the extrapolation method of Carro-Martin, which generalizes the work of Antonov and Arias-de-Reyna.Comment: 18 pages. v2: Several typos corrected. Final version of the paper, accepted to LM

Quaero@H1: An Interface to High-pT HERA Event Data

Distributions from high-pT HERA event data analyzed in a general search for new physics at H1 have been incorporated into Quaero, an algorithm designed to automate tests of specific hypotheses with high energy collider data. The use of Quaero@H1 to search for leptoquarks, R-parity violating supersymmetry, and excited quarks provides examples to develop intuition for the algorithm's performance.Comment: Submitted to Eur. Phys. J.