Results 181 to 190 of about 111,047 (227)
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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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Geodesics in Heisenberg Groups
Geometriae Dedicata, 1997For the Heisenberg group \(H^{2n+1}\) the author defines a left-invariant metric and computes the Levi-Civita connection and the curvature tensor. He also determines the isotropy subgroup \( \text{Iso}_0(H^{2n+1}) \). Then, equations for geodesics in \(H^{2n+1}\) are given which simplify considerably for ``horizontal'' lines.
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1997
Abstract The Heisenberg group is a nilpotent Lie group ‒ or rather a family of Lie groups, one for each odd dimension ≥ 3 ‒ which have many features in common with Euclidean spaces.
Guy David, Stephen Semmes
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Abstract The Heisenberg group is a nilpotent Lie group ‒ or rather a family of Lie groups, one for each odd dimension ≥ 3 ‒ which have many features in common with Euclidean spaces.
Guy David, Stephen Semmes
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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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Journal of Physics A: Mathematical and General, 1993
Summary: The Heisenberg algebra \(h(3)\) is the Lie algebra of the Lie group \(H(3)\) of \(3\times 3\) upper triangular matrices with the 1's on the diagonal. This group is quantized. The dual algebra \(h(3)^*\) is also quantized, resulting in a quantum coadjoint representation of the quantum group \(H(3)_{a,b,c, d,m,n}\).
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Summary: The Heisenberg algebra \(h(3)\) is the Lie algebra of the Lie group \(H(3)\) of \(3\times 3\) upper triangular matrices with the 1's on the diagonal. This group is quantized. The dual algebra \(h(3)^*\) is also quantized, resulting in a quantum coadjoint representation of the quantum group \(H(3)_{a,b,c, d,m,n}\).
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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 \({\cal H}\).
Anton Deitmar, Siegfried Echterhoff
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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 \({\cal H}\).
Anton Deitmar, Siegfried Echterhoff
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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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2001
Abstract The Heisenberg Group and its Fundamental Representation Associated with the symplectic phase space V is the Heisenberg group. This matrix group is defined over Z, and gives the extension of Heis to characteristic 2. We prefer to keep the symmetric form of Heis, which shows more clearly the symmetry between x and y, ‘position ...
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Abstract The Heisenberg Group and its Fundamental Representation Associated with the symplectic phase space V is the Heisenberg group. This matrix group is defined over Z, and gives the extension of Heis to characteristic 2. We prefer to keep the symmetric form of Heis, which shows more clearly the symmetry between x and y, ‘position ...
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The Heisenberg group andK-theory
K-Theory, 1993A unifying proof of Bott periodicity and that of the Connes isomorphism theorem is given using continuous fields of \(C^*\)-algebras. The last theorem asserts that for each \(C^*\)-dynamical system \((A,\alpha)\) there is a canonical isomorphism of Abelian groups \(K_ *(A\rtimes_ \alpha\mathbb{R})\to K_{*+1}(A)\).
Elliott, George Arthur +2 more
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Generalized Weyl–Heisenberg (GWH) groups
Analysis and Mathematical Physics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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