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ON THE QUADRATIC HEISENBERG GROUP
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2010In this paper we introduce the quadratic Weyl operators canonically associated to the one mode renormalized square of white noise (RSWN) algebra as unitary operator acting on the one mode interacting Fock space {Γ, {ωn, n ∈ ℕ}, Φ} where {ωn, n ∈ ℕ} is the principal Jacobi sequence of the nonstandard (i.e. neither Gaussian nor Poisson) Meixner classes.
ACCARDI, LUIGI, Ouerdiane, H, Rebei, H.
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Annali di Matematica Pura ed Applicata, 2019
In this paper, we consider the semilinear Cauchy problem for the heat equation with power nonlinearity in the Heisenberg group Hn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb ...
V. Georgiev, A. Palmieri
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In this paper, we consider the semilinear Cauchy problem for the heat equation with power nonlinearity in the Heisenberg group Hn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb ...
V. Georgiev, A. Palmieri
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2014
In this chapter we prove the Stone-von Neumann Theorem, which gives a full characterization of the unitary dual of the Heisenberg group \({\cal H}\). We then apply the trace formula to describe the spectral decomposition of \({L^2}(\Lambda \backslash H)\), where π is the standard integer lattice in \({\cal H}\).
Siegfried Echterhoff, Anton Deitmar
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In this chapter we prove the Stone-von Neumann Theorem, which gives a full characterization of the unitary dual of the Heisenberg group \({\cal H}\). We then apply the trace formula to describe the spectral decomposition of \({L^2}(\Lambda \backslash H)\), where π is the standard integer lattice in \({\cal H}\).
Siegfried Echterhoff, Anton Deitmar
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Optimization in the Heisenberg group
Optimization, 2006In this article, the local unconstrained and the constrained optimization problems in the Heisenberg group are investigated. The framework on which we work is given by the class of weakly H-convex functions recently introduced in the literature. This geometric notion of convexity, that is strictly related to the stratified structure of the group and ...
CALOGERO, ANDREA GIOVANNI +2 more
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A Hardy type inequality on fractional order Sobolev spaces on the Heisenberg group
, 2018In this paper, we derive a non linear Hardy type inequality on certain fractional order Sobolev spaces on the Heisenberg group. Our inequality is an analogous version of an inequality of the same name on weighted Folland-Stein spaces which had been ...
A. Adimurthi, Arka Mallick
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1992
For the introductory remarks of this chapter let us assume that L is a very ample line bundle on an abelian variety X = V/Λ and φ L : X ↪ ℙ N the associated embedding. Recall the group K(L) consisting of all x ∈ X with t x * L≃L. We will see that the translations of X by elements of K(L) extend to linear automorphisms of ℙ N .
Herbert Lange, Christina Birkenhake
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For the introductory remarks of this chapter let us assume that L is a very ample line bundle on an abelian variety X = V/Λ and φ L : X ↪ ℙ N the associated embedding. Recall the group K(L) consisting of all x ∈ X with t x * L≃L. We will see that the translations of X by elements of K(L) extend to linear automorphisms of ℙ N .
Herbert Lange, Christina Birkenhake
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Random walks and random tug of war in the Heisenberg group
Mathematische Annalen, 2018We study mean value properties of $$\mathbf{p }$$ p -harmonic functions on the first Heisenberg group $${\mathbb {H}}$$ H , in connection to the dynamic programming principles of certain stochastic processes.
M. Lewicka, J. Manfredi, D. Ricciotti
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2015
This chapter is meant to give a brief and by no means complete description of the Heisenberg group \(\mathbb {H}\), that will be the setting of this work. Customarily this group is presented as a particular group on \(\mathbb {R}^3\). This is not restrictive and to explain why we recall some definitions and basic properties of Carnot groups in order to
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This chapter is meant to give a brief and by no means complete description of the Heisenberg group \(\mathbb {H}\), that will be the setting of this work. Customarily this group is presented as a particular group on \(\mathbb {R}^3\). This is not restrictive and to explain why we recall some definitions and basic properties of Carnot groups in order to
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2017
One of the big contributions of E. M. Stein is the development of harmonic analysis on the Heisenberg group. In a fundamental joint paper with G. B. Folland, Stein laid all the groundwork for this study. In this chapter we reproduce and develop some of that groundwork.
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One of the big contributions of E. M. Stein is the development of harmonic analysis on the Heisenberg group. In a fundamental joint paper with G. B. Folland, Stein laid all the groundwork for this study. In this chapter we reproduce and develop some of that groundwork.
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Analysis on the Heisenberg Group
2009Here we build on the material in Chapter 3 to prove some fairly profound results about the boundedness of the Szegő integral operator on the boundary of the unit ball. All the key ideas about singular integrals, homogeneous dimension, the Calderon-Zygmund theory, and interpolation of operators come into play.
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