1,720,983 research outputs found
Oscillating multipliers on rank one symmetric spaces
No full textIn this paper we consider the family m_{α,β} of radial multipliers on rank one symmetric spaces G/K of the non compact type, defined by the formula
m_{α,β}(λ)=(λ2+ρ2)^(-β/2) exp(i((λ2+ρ2)^(α/2)), Reβ≥0, α>0.
Let T_{α,β} denote the associated convolution operator. Our main result is the following:
if α > 1, T_{α,β} is bounded on L^p(G/K) if and only if p=2;
if α < 1, T_{α,β} is bounded on L^p(G/K) if |1/p-1/2| < Reβ/(α dim(G/K));
if α = 1, T_{α,β} is bounded on L^p(G/K) if |1/p-1/2| < Reβ/(dim(G/K)−1).
The values α=1 and α=1 are of particular interest, since che corresponding operators are closely related to the wave and the Schrödinger equations on G/K, the elliptic part of them being given by the Laplace-Beltrami operator.
The case α>1 differs considerably from the corresponding Euclidean result and this fact is a consequence of the properties of the spherical Fourier transform on symmetric spaces. On the other side, the results for α≤1 resemble closely the Euclidean ones because “the part at infinity” of T_{α,β} behaves nicely, while the “local part” is assentially Euclidean
Endpoint estimates for first-order Riesz transforms associated to the Ornstein-Uhlenbeck operator
No full textIn the setting of Euclidean space with the
Gaussian measure g, we consider all first-order
Riesz transforms associated to the infinitesimal generator of
the Ornstein-Uhlenbeck semigroup. These operators are known to be
bounded on L^p(g), for
1<p<\infty. We determine which of them are bounded from H^1(g) to
L^1(g) and from L^\infty(g)$ to \BMO(g). Here H^1(g) and BMO(g)
are the spaces introduced in this setting by the first two authors. Surprisingly, we find that the results depend on the dimension
of the ambient space
Lp-Lq estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. I
No full textLet X = G/K be a symmetric space of noncompact type, L be the Laplace-Beltrami operator
on X, and b the bottom of its spectrum. In this paper we study the Lp-Lq mapping properties
of several families of operators naturally associated with L:
θ-heat semigroup, H_{t,θ) = exp(tL−θb),
complex powers of resolvent operator, H^α_θ=(L−θb)^{−α/2}, and
S^α_θ = (L−θb)^{−α/2} exp(i(L−θb)), where 0≤θ≤1, Reα≥ 0, closely related to the Cauchy problem for the Schrodinger operator on X. The
techniques mix harmonic analysis on semisimple Lie groups (Plancherel measure, c-function) and
functional analysis (interpolation, semigroup theory).
One of the contribution in this paper is to give precise estimates for the Lp-Lq operator norm of H_{t,θ) for large time t on all noncompact symmetric spaces. These estimates show that the interpolation and extrapolation methods of ultracontractivitywhich work well for small t or on groups of polynomial growth are not applicable here; in particular, log(|||H_{t,θ)|||_{p,q}) does not depend linearly on 1/p and 1/q
Lp-Lq estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. II
No full textLet X = G/K be a symmetric space of noncompact type, L be the Laplace-Beltrami operator on X, and b the bottom of its spectrum. In this paper we study the behaviour of the Lp-Lq operator norms of the (σ,θ)-Poisson semigroup as t tends to zero and to infinity for all such p and q. As t tends to infinity the behaviour of these norms involves power of t in which the rank (r) and the pseudo-dimension of X play an important role. Two features of our study are noteworthy. First, while the θ-heat semigroup is Lp-Lq bounded whenever 1≤p≤q≤∞, the (σ,θ)-Poisson semigroup is not Lp-Lq bounded for many such p and q. Second, when p and q reach the critical index for Lp-Lq boundedness, the exponent r+1 appears
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Get PDF“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
Get PDFWe 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
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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