Search results for "Manifold"

Closed star products and cyclic cohomology

1992

We define the notion of a closed star product. A (generalized) star product (deformation of the associative product of functions on a symplectic manifold W) is closed iff integration over W is a trace on the deformed algebra. We show that for these products the cyclic cohomology replaces the Hochschild cohomology in usual star products. We then define the character of a closed star product as the cohomology class (in the cyclic bicomplex) of a well-defined cocycle, and show that, in the case of pseudodifferential operators (standard ordering on the cotangent bundle to a compact Riemannian manifold), the character is defined and given by the Todd class, while in general it fails to satisfy t…

Analytic Bergman operators in the semiclassical limit

2018

Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted $L^2$ spaces with analytic weights, and show that their kernel functions admit an asymptotic expansion in the class of analytic symbols. As a corollary, we obtain new estimates for asymptotic expansions of the Bergman kernel on $\mathbb{C}^n$ and for high powers of ample holomorphic line bundles over compact complex manifolds.

On the representation of integers by indefinite binary Hermitian forms

2011

Given an integral indefinite binary Hermitian form f over an imaginary quadratic number field, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most s by f, as s tends to infinity.

Assouad dimension, Nagata dimension, and uniformly close metric tangents

2013

We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the dimensions of its metric tangents. Having uniformly close tangents is not sufficient. What is needed in addition is either that the tangents have dimension with uniform constants independent from the point and the tangent, or that the tangents are unique. We will apply our results to equiregular subRiemannian manifolds and show that locally their Nagata dimension equals the to…

THE BISHOP-PHELPS-BOLLOBAS PROPERTY FOR HERMITIAN FORMS ON HILBERT SPACES

2013

Gaussian surface measures and the radon transform on separable banach spaces

1980

Multi-commutation in spectrometry

2009

We review recent developments in manifold components and the introduction of light-emitting-diode technology in spectroscopic detection in order to evaluate the tremendous possibilities offered by multi-commutation for in-field and in-situ measurements, based on the use of multi-pumping and low-voltage, portable batteries, which make possible a dramatic reduction in size, weight and power requirements of spectrometric devices.

Renormalization-group analysis for the transition to chaos in Hamiltonian systems

2002

Abstract We study the stability of Hamiltonian systems in classical mechanics with two degrees of freedom by renormalization-group methods. One of the key mechanisms of the transition to chaos is the break-up of invariant tori, which plays an essential role in the large scale and long-term behavior. The aim is to determine the threshold of break-up of invariant tori and its mechanism. The idea is to construct a renormalization transformation as a canonical change of coordinates, which deals with the dominant resonances leading to qualitative changes in the dynamics. Numerical results show that this transformation is an efficient tool for the determination of the threshold of the break-up of…

Contribution à l’apprentissage de représentation de données à base de graphes avec application à la catégorisation d’images

2020

Graph-based Manifold Learning algorithms are regarded as a powerful technique for feature extraction and dimensionality reduction in Pattern Recogniton, Computer Vision and Machine Learning fields. These algorithms utilize sample information contained in the item-item similarity and weighted matrix to reveal the intrinstic geometric structure of manifold. It exhibits the low dimensional structure in the high dimensional data. This motivates me to develop Graph-based Manifold Learning techniques on Pattern Recognition, specially, application to image categorization. The experimental datasets of thesis correspond to several categories of public image datasets such as face datasets, indoor and…

Markovian Connection, Curvature and Weitzenböck Formula on Riemannian Path Spaces

2001

Abstract We shall consider on a Riemannian path space P m o ( M ) the Cruzeiro–Malliavin's Markovian connection. The Laplace operator will be defined as the divergence of the gradient. We shall compute explicitly the associated curvature tensor. A Weitzenbock formula will be established. To this end, we shall introduce an “inner product” between the tangent processes and simple vector fields.