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On the supremum of a family of set functions
(2023)The concept of supremum of a family of set functions was introduced by M. Veraar and I. Yaroslavtsev (2016) for families of measures defined on a measurable space. We expand this concept to include families of set functions ... -
Quadratic variation for cylindrical martingale-valued measures
(2023)This article focuses in the definition of a quadratic variation for cylindrical orthogonal martingale-valued measures defined on Banach spaces. Sufficient and necessary conditions for the existence of such a quadratic ... -
The Sparse T1 Theorem [presentación]
(2017-03) -
Lacunary discrete spherical maximal functions
(2019)We prove new l^p(Z^d) bounds for discrete spherical averages in dimensions d greater than or equal to 5. We focus on the case of lacunary radii, first for general lacunary radii, and then for certain kinds of highly ... -
Characterization of two-parameter matrix valued BMO by commutator with the Hilbert Transform
(2018)In this paper, we prove that the space of two parameter matrix-valued BMO functions can be characterized by considering iterated commutators with the Hilbert transform. The upper estimate relies on Petermichl's representation ... -
The Sparse T1 Theorem
(2017)We impose standard T1-type assumptions on a Calderon-Zygmund operator T, and deduce that for bounded compactly supported functions f and g there is a sparse bilinear form B so that |< Tf, g >|; < B(f,g). The proof is short ... -
A nonlinear relapse model with disaggregated contact rates: Analysis of a forward-backward bifurcation
(2023-09)Throughout the progress of epidemic scenarios, individuals in different health classes are expected to have different average daily contact behavior. This contact heterogeneity has been studied in recent adaptive models ... -
Riemannian manifolds in noncommutative geometry
(2012-07)We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin^c manifolds; and conversely, ... -
An overlapping preconditioner for 2D virtual problems posed in H(rot) with irregular subdomains
(2022)We present a two-level overlapping Schwarz preconditioner for problems posed in H(rot) in two dimensions, that extends previous methods for Nédélec elements (triangular meshes) to general polygonal partitions (virtual ... -
Exact phase space functional for two-body systems
(2010-11-21)The determination of the two-body density functional from its one-body density is achieved for Moshinsky's harmonium model, using a phase-space formulation, thereby resolving its phase dilemma. The corresponding sign rules ... -
Quantum gauge models without classical Higgs mechanism
(2010-09-15)We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. The BRST formulation of gauge invariance in ... -
Reconstruction of manifolds in noncommutative geometry
(2008-01-31)We show that the algebra A of a commutative unital spectral triple (A,H,D) satisfying several additional conditions, slightly stronger than those proposed by Connes, is the algebra of smooth functions on a compact spin manifold. -
Fourier analysis on the affine group, quantization and noncompact Connes geometries
(2008-04)We find the Stratonovich-Weyl quantizer for the nonunimodular affine group of the line. A noncommutative product of functions on the half-plane, underlying a noncompact spectral triple in the sense of Connes, is obtained ... -
A two-step estimation procedure for locally stationary ARMA processes with tempered stable innovations
(2023-03)The class of locally stationary processes assumes a time-varying (tv) spectral representation and finite second moment. Different areas have observed phenomena with heavy tail distributions or infinite variance. Using ... -
Teaching basic statistics to blind students
(2017)Understanding statistics has become extremely important not only for researchers but also for the general public in order to understand publications that include statistical analysis. Having in mind promoting ... -
Orbifolds are not commutative geometries
(2008)In this note we show that the crucial orientation condition for commutative geometries fails for the natural commutative spectral triple of an orbifold M/G. -
Dixmier traces on noncompact isospectral deformations
(2006)We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group R^l. Under deformation by a torus action, a ... -
Combinatorics of renormalization as matrix calculus
(2006)We give a simple presentation of the combinatorics of renormalization in perturbative quantum field theory in terms of triangular matrices. The prescription, that may be of calculational value, is derived from first ... -
Indirect inference for locally stationary ARMA processes with stable innovations
(2020)The class of locally stationary processes assumes that there is a time-varying spectral representation, that is, the existence of finite second moment. We propose the α-stable locally stationary process by modifying the ... -
The local index formula for SU_q(2)
(2005)We discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as ...
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