1,721,249 research outputs found
Strichartz estimates for the Schroedinger equation for the sublaplacian on complex spheres
No full textAbstract. In this paper we consider the sublaplacian L on the unit complex sphere S^(2n+1)
C^(n+1), equipped with its natural CR structure, and derive Strichartz estimates with fractional
loss of derivatives for the solutions of the free Schrodinger equation associated with L. Our results
are stated in terms of certain Sobolev-type spaces, that measure the regularity of functions
on S^(2n+1) dierently according to their spectral localization. Stronger conclusions are obtained
for particular classes of solutions, corresponding to initial data whose spectrum is contained in
a proper cone of N^2
Regularity of projection operators attached to worm domains
No full textThis paper considers the non-smooth unbounded worm domains
Dβ={(z1,z2)∈C2:Re(z1e−ilogz2z⎯⎯⎯2)>0,|logz2z⎯⎯2|<β−π2},
where β>π2. These model domains were important when the first author [Acta Math. 168 (1992), no. 1-2, 1–10; MR1149863] used them to show that on the Diederich-Fornæss worm domains [K. Diederich and J. E. Fornæss, Math. Ann. 225 (1977), no. 3, 275–292; MR0430315] the Bergman projection does not map the Sobolev space Wk into itself when k≥π/(total amount of winding). In the paper under review, the authors construct an oblique projection operator on Dβ which preserves the level of the Sobolev spaces. More precisely, let
L2j(Dβ)={f∈L2(Dβ):f∘ρθ=eijθf},
where ρθ=(z1,eiθz2) is a rotation on Dβ. Define Bj(Dβ):=L2j(Dβ)∩{holomorphic functions on Dβ}, Wsj(Dβ):=L2j(Dβ)∩Ws(Dβ), and Ws(Dβ) the closure of :=C∞0(Dβ) in Ws(Dβ). The main theorem of the paper shows that for all j∈Z there exists a bounded linear projection Tj:=L2(Dβ)→Bj(Dβ)
which satisfies Tj:Ws(Dβ)→Wsj(Dβ)for every s≥0
New results on the Bergman kernel of the worm domain in complex space
No full textWe study the Bergman kernel and projection on the worm domains for β > π. We calculate the kernels explicitly, up to an error term that can be controlled. Denote by P the Bergman projection on Dβ and by P′ the one on D′β. We show that is bounded when 1 < p < ∞, while if and only if 2/(1 + vβ) < p < 2/(1 - vβ), where vβ = π/(2β - π). Along the way, we give a new proof of the failure of Condition R on these worms. Finally, we are able to show that the singularities of the Bergman kernel on the boundary are not contained in the boundary diagonal
L^p-spectral multipliers for the Hodge Laplacian acting on 1-forms on the Heisenberg group
No full textWe prove that, if Δ_1 is the Hodge Laplacian acting on differential 1-forms on the (2n+1)-dimensional Heisenberg group, and if m is a Mihlin-Hörmander multiplier on the positive half-line, with L^2-order of smoothness greater than n+1/2, then m(Δ_1) is L^p-bounded for 1 < p < infinity. Our approach leads to an explicit description of the spectral decomposition of Δ_1 on the space of L^2-forms in terms of the spectral analysis of the sub-Laplacian L and the central derivative T, acting on
scalar-valued functions
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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