33,290 research outputs found
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.
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