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    Bochner-Riesz means of functions in weak-Lp

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    The Bochner-Riesz means of order δ≥0 for suitable test functions on RN are defined via the Fourier transform by {Mathematical expression}. We show that the means of the critical index {Mathematical expression}, do not map Lp,∞(RN) into Lp,∞(RN), but they map radial functions of Lp,∞(RN) into Lp,∞(RN). Moreover, if f is radial and in the Lp,∞(RN) closure of test functions, SRδf(x) converges, as R→+∞, to f(x) in norm and for almost every x in RN. We also observe that the means of the function |x|-N/p, which belongs to Lp,∞(RN) but not to the closure of test functions, converge for no x

    Going Beyond Counting First Authors in Author Co-citation Analysis

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    The present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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