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Showing 1 to 14 of 14 for “"Heisenberg group"”.
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Projections, slicings and Fourier transforms in the Heisenberg group
… study of projection and slicing problems in the Heisenberg group from the point of view of Hausdorff dimension distortion. It then gives a short summary of research done in this area up to date before introducing and explaining my own contributions to it. Finally, the group Fourier transform in …
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Weyl Pseudodifferential Calculus and the Heisenberg Group in New Settings
… both Weyl pseudodifferential calculus and the Heisenberg group in new settings, through two published papers and a chapter representing work towards a construction of Haar bases of unimodular LC groups. We finish with some remarks about an extension of both Heisenberg group and …
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Adams inequalities with exact growth condition : on Rn and the Heisenberg group
… equation. Lastly, we extend our result to the Heisenberg group. By applying the same technique used in R[superscript n], we derive a sharp Adams inequality with critical growth condition on H[superscript n] for integral operators whose kernels are strictly Riesz-like on H[superscript n]. As a …
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Geometric mapping theory of the Heisenberg group, sub-Riemannian manifolds, and hyperbolic spaces
We discuss the Heisenberg group $\Heis^n$ and its mappings from three perspectives. As a nilpotent Lie group, $\Heis^n$ can be viewed as a generalization of the real numbers, leading to new notions of base-$b$ expansions and continued fractions. As a metric space, $\Heis^n$ serves as an …
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Nodal geometry of eigenfunctions on smooth manifolds and hardy-littlewood-sobolev inequalities on the heisenberg group
… its sharp version.</p> <p>Part II: O the Heisenberg group with homogeneous dimension Q=2n+2, we study the Hardy-Littlewood-Sobolev (HLS) inequality,</p> <p>and particularly its sharp version. Weighted Hardy-Littlewood-Sobolev inequalities with different weights shall also be investigated, …
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Analysis in the Heisenberg group: weak s-John domains and the dimensions of graphs of Holder functions
… and analytic properties in sub-Riemannian Carnot groups. We introduce weak s-John domains, in analogy with weak John domains, and we prove that weak s-John is equivalent to a localized version. This is applied in showing that a bounded C^{1,alpha} domain in R^3 will be a weak s-John domain in the …
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Intrinsic Lipschitz graphs in Heisenberg groups and non linear sub-elliptic PDEs
… Moreover we study the obstacle problem in the Heisenberg group and we prove a geometric Poincarè inequality for a class of semilinear equations in the Engel group.
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Zero Divisors, Group Von Neumann Algebras and Injective Modules
… representations of the generalized Wyle-Heisenberg group in 𝑛² dimensions and its relations with Gabor's question from Gabor Analysis in the light of the time-frequency equation. We study the zero divisor conjecture in relation to the reduced 𝐶*-algebras and operator norm 𝐶*-algebras. For …
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Laplacians on Nonisotropic Heisenberg Groups with Multi-Dimensional Center
… begin with the construction of the nonisotropic Heisenberg group with multi- dimensional center. The sub-Laplacian on it is introduced. By taking the inverse Fourier transform of the sub-Laplacian with respect to the center, we get a family of twisted Laplacians. They are proved to be globally …
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The Space of Left Orders on a Group
The study of orderable groups is a topic that is all too often overlooked as a topic in algebra. The subject of orderable groups is a field of study which is directly associated with algebraic group theory, algebraic topology, and set theory. This paper will act as a guide into the world of …
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Monotonicity Formulas for Diffusion Operators on Manifolds and Carnot Groups, Heat Kernel Asymptotics and Wiener's Criterion on Heisenberg-type Groups
… geometry, with a special focus on the Heisenberg group Hn, Heisenbergtype (H-type) groups, and Carnot groups.</p> <p>As we wish for this thesis to be relatively self-contained, the main definitions and background are covered in Chapter 1. This includes basic information about Carnot …
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New Characterizations Of Sobolev Spaces On Heisenberg And Carnot Groups And High Order Sobolev Spaces On Eucliean Spaces
… an in-depth study of Sobolev spaces on Heisenberg groups, as well as Carnot groups, second order and high order Sobolev spaces on Euclidean spaces.</p>
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Universality of Cutoff for Random Walks on Random Cayley Graphs
Consider the random Cayley graph of a finite group G with respect to k generators chosen uniformly at random. This draws a Cayley graph uniformly amongst all degree-k Cayley graphs of G. A conjecture of Aldous and Diaconis (1985) from the '80s asserts, for k ≫ log |G|, the following: • the random …
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New and old sub-Riemannian challenges bridging analysis and geometry
… theory for almost perimeter minimizers in Carnot groups. 4 Geometry of hypersurfaces in Heisenberg groups.