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In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space equipped with the homogeneous Sobolev metric of order one is a flat space in the sense of Riemannian geometry, as it is isometric to an ...
We prove a fixed point theorem for a family of Banach spaces, notably for L^1. Applications include the optimal answer to the "derivation problem" for group algebras which originated in the 1960s. ...
Attention is crucial for visual perception because it allows the visual system to effectively use its limited resources by selecting behaviorally and cognitively relevant stimuli from the large amount of information impinging on the eyes. Reflexive, stimul ...
The aim of my presentation is to communicate results of an exploratory stage of my research. I will briefly cover the research design, followed by a summary of the understandings of space that I use to structure the presentation. Then I will discuss some r ...
We prove that the multiplier algebra of the Drury-Arveson Hardy space H-n(2) on the unit ball in C-n has no corona in its maximal ideal space, thus generalizing the corona theorem of L. Carleson to higher dimensions. This result is obtained as a corollary ...
For a mapping between Banach spaces, two weaker variants of the usual notion of asymptotic linearity are defined and explored. It is shown that, under inversion through the unit sphere, they correspond to Hadamard and weak Hadamard differentiability at the ...
The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying siz ...
As Avez showed (in 1970), the fundamental group of a compact Riemannian manifold of nonpositive sectional curvature has exponential growth if and only if it is not flat. After several generalizations from Gromov, Zimmer, Anderson, Burger and Shroeder, the ...
The subject of this thesis lies in the intersection of differential geometry and functional analysis, a domain usually called global analysis. A central object in this work is the group Ds(M) of all orientation preserving diffeomorphisms of a compact manif ...
This paper revisits theories of weak signal analysis using the concepts of 'framing' and 'meta-framing' to provide an enriched methodological environment for management and decision-making in turbulent contexts. This attempt takes place within the effort t ...
