1,720,972 research outputs found
Functional Calculus on Homogeneous Groups
Get PDFDati degli operatori differenziali congiuntamente ipoellittici, formalmente autoaggiunti, omogenei ed invarianti a sinistra L_1,..., L_n su un gruppo stratificato G, si considera la trasformata nucleo K ad essi associata. Vengono presentati su gruppi di Heisenberg degli esempi relativi allo studio delle proprietà: (RL) se K(m) è integrabile, allora m è continua; (S) se K(m) è di Schwartz, allora m è di Schwartz
Spectral Multipliers on 2-Step Stratified Groups, II
Get PDFGiven a graded group G and commuting, formally self-adjoint, left-invariant, homogeneous differential operators L_1,..., L_n on G, one of which is Rockland, we study the convolution operators m(L_1,..., L_n) and their convolution kernels, with particular reference to the case in which G is abelian and n=1, and the case in which G is a 2-step stratified group which satisfies a slight strengthening of the Moore-Wolf condition and L_1,..., L_n are either sub-Laplacians or central elements of the Lie algebra of G.
Under suitable conditions, we prove that: i) if the convolution kernel of the operator m(L_1,..., L_n) belongs to L^1, then m equals almost everywhere a continuous function vanishing at infinity (`Riemann-Lebesgue lemma'); ii) if the convolution kernel of the operator m(L_1,..., L_n) is a Schwartz function, then m equals almost everywhere a Schwartz function
Weighted sub-Laplacians on M\'etivier Groups: Essential Self-Adjointness and Spectrum
Get PDFLet be a M\'etivier group and let be any homogeneous norm on . For
denote by the function and consider the
weighted sub-Laplacian associated with the Dirichlet
form ,
where is the horizontal gradient on . Consider
with domain . We prove that
is essentially self-adjoint when . For
a particular , which is the norm appearing in 's fundamental
solution when is an H-type group, we prove that
has purely discrete spectrum if and only if , thus proving a
conjecture of J. Inglis.Comment: 15 pages; to appear on Proc. Amer. Math. So
Asymptotics for the Heat Kernel on H-Type Groups
Get PDFWe give sharp asymptotic estimates at infinity of all radial partial
derivatives of the heat kernel on H-type groups. As an application, we give a
new proof of the discreteness of the spectrum of some natural sub-Riemannian
Ornstein-Uhlenbeck operators on these groups.Comment: 29 pages; submitte
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
Moltiplicatori spettrali su gruppi omogenei
Get PDFPresi degli operatori differenziali omogenei, formalmente autoaggiunti, congiuntamente ipoellittici ed invarianti a sinistra L_1,..., L_n su un gruppo omogeneo G, si considera la trasformata nucleo K ad essi associata. Si studiano, nel contesto dei gruppi abeliani e dei gruppi di Heisenberg, le proprietà: (RL) se K(m) è integrabile, allora m è continua; (S) se K(m) è di Schwartz, allora m è di Schwartz
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
A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics II
Get PDFWe continue the study of the space of functions with
bounded fractional variation in and of the distributional
fractional Sobolev space , with
and , considered in the previous works arXiv:1809.08575 and
arXiv:1910.13419. We first define the space and establish
the identifications and
, where
and are the (real) Hardy space and the Bessel
potential space, respectively. We then prove that the fractional gradient
strongly converges to the Riesz transform as for
and functions. We also study the
convergence of the -norm of the -rescaled fractional gradient of
functions. To achieve the strong limiting behavior of
as , we prove some new fractional interpolation
inequalities which are stable with respect to the interpolating parameter.Comment: 43 page
A Note on Hardy Spaces on Quadratic CR Manifolds
Get PDFGiven a quadratic CR manifold embedded in a complex space, and
a holomorphic function on a tubular neighbourhood of , we show
that the -norms of the restriction of to the translates of
is decreasing for the ordering induced by the closed convex
envelope of the image of the Levi form of .Comment: 6 pages, no figure
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