1,721,108 research outputs found
Some Norm Bounds for the Spectral Projections of the Heisenberg Sublaplacian
No full textThis paper is a summary of the lectures delivered by the author at the Gent Summer School in Analysis and PDE in September 2023. It concerns the boundedness of the generalized spectral projections associated to the sublaplacian in the Heisenberg group, seen as operators from L^1_t L^p_z to L^1_\infty L^q_z. A conjecture about the range of p,q for which the projections are bounded is formulated and some motivations are provided
On Octonionic Harmonic Projection Operators
No full textHarmonic projection operators map square integrable functions on a sphere onto subspaces of spherical harmonics. Let Sdn−1 denote the unit sphere in Rdn, with d∈{1,2,4,8}. In this paper, we start to study these projectors in the octonionic setting, that is, when d=8 and n=2. We also formulate a conjecture about the norm of harmonic projection operators, considered as operators from Lp(Sdn−1) onto L2(Sdn−1), for 1≤p≤2 and d∈{1,2,4,8}
Special functions and rod nonlinear theory
No full textThere are many physical models or theories in which some functions appear in natural and regular fashion, starting with polynomials and algebraic functions and progressing through the “elementary” transcendental ones, almost all already known to the ancients. Most of special functions of Mathematical Physics are generated from the study of those ordinary differential equations (ODEs) in which the separation of variables breaks many categories of linear partial differential equations, mainly that of Laplace. Among the many special functions that satisfy these second order ODEs the people find the polynomials which bear the names of Tchebychev, Hermite, Jacobi, Laguerre, and the Whittaker functions, and the parabolic cylinder functions. However, there are further special functions not stemming from second order linear ODEs. The problem of “rectification of quadratures” was generally encountered in the setting of ODEs that cannot be solved in closed algebraic form or “by quadratures”
Time-Frequency Analysis and Metaplectic Operators
No full textWe perform a time-frequency analysis using metaplectic operators as
main protagonists of this field. By means of metaplectic operators we are able
to define the most famous time-frequency representations, such as the short-time
Fourier transform (STFT), the .τ-Wigner distributions, the ambiguity function, and
many others. We call them the metaplectic Wigner distributions.
In particular, the ones enjoying the so-called shift-invertibility property charac-
terize modulation and Wiener amalgam spaces, replacing the STFT in their norms.
Finally, we introduce new frames, called metaplectic Gabor frames, as natural
generalizations of Gabor frames in the framework of metaplectic Wigner distribu-
tions.
These metaplectic distributions (and related frames) provide meaningful def-
initions of local frequencies: they can be used to effectively measure the local
frequency content of signals. Further applications are the study of the phase-space
concentration of Schrödinger equations with bounded perturbations.
This approach could pave the way to new quantization procedures
Quasi-symmetrizer and hyperbolic equations
No full textGiven a matrix A, a symmetrizer for A is a symmetric matrix Q such that QA is symmetric. The symmetrizer is a useful tool to obtain a-priori estimates for the solutions to hyperbolic equations. If Q is not positive definite, it is more convenient to consider a quasi-symmetrizer: a sequence of symmetric and positive defined matrices {Qε}ε∈]0,1] such that QεA approaches a symmetric matrix.
In these notes we make a short survey of the basic notions of symmetrizer and quasi-symmetrizer and we give some applications to the well-posedness for the hyperbolic Cauchy problem
Potential theory results for a class of PDOs admitting a global fundamental solution
Full text linkWe outline several results of Potential Theory for a class of linear par-tial differential operators L of the second order in divergence form. Under essentially the sole assumption of hypoellipticity, we present a non-invariant homogeneous Harnack inequality for L; under different geometrical assumptions on L (mainly, under global doubling/Poincaré assumptions), it is described how to obtainan invariant, non-homogeneous Harnack inequality. When L is equipped with a global fundamental solution Γ, further Potential Theory results are available (such as the Strong Maximum Principle). We present some assumptions on L ensuring that such a Γ exists
Chapter 7 Cauchy problem for some 2×2 hyperbolic systems of pseudo-differential equations with nondiagonalisable principal part
No full text
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
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