1,704 research outputs found
Balian-Low Theorems in Several Variables
Recently, Nitzan and Olsen showed that Balian-Low theorems (BLTs) hold for
discrete Gabor systems defined on . Here we extend these results
to a multivariable setting. Additionally, we show a variety of applications of
the Quantitative BLT, proving in particular nonsymmetric BLTs in both the
discrete and continuous setting for functions with more than one argument.
Finally, in direct analogy of the continuous setting, we show the Quantitative
Finite BLT implies the Finite BLT.Comment: To appear in Approximation Theory 16 conference proceedings volum
CR embeddings of CR manifolds
We improve results of Baouendi, Rothschild and Treves and of Hill and Nacinovich by finding a much weaker sufficient condition for a CR manifold of type (n, k) to admit a local CR embedding into a CR manifold of type (n+ ℓ, k- ℓ). While their results require the existence of a finite dimensional solvable transverse Lie algebra of vector fields, we require only a finite dimensional extension
Experimental Identification of the Kink Instability as a Poloidal Flux Amplification Mechanism for Coaxial Gun Spheromak Formation
The magnetohydrodynamic kink instability is observed and identified
experimentally as a poloidal flux amplification mechanism for coaxial gun
spheromak formation. Plasmas in this experiment fall into three distinct
regimes which depend on the peak gun current to magnetic flux ratio, with (I)
low values resulting in a straight plasma column with helical magnetic field,
(II) intermediate values leading to kinking of the column axis, and (III) high
values leading immediately to a detached plasma. Onset of column kinking agrees
quantitatively with the Kruskal-Shafranov limit, and the kink acts as a dynamo
which converts toroidal to poloidal flux. Regime II clearly leads to both
poloidal flux amplification and the development of a spheromak configuration.Comment: accepted for publication in Physical Review Letter
Lp Fourier multipliers on compact Lie groups
In this paper we prove Lp multiplier theorems for invariant and non-invariant
operators on compact Lie groups in the spirit of the well-known
Hormander-Mikhlin theorem on Rn and its variants on tori Tn. We also give
applications to a-priori estimates for non-hypoelliptic operators. Already in
the case of tori we get an interesting refinement of the classical multiplier
theorem.Comment: 22 pages; minor correction
Spectral multipliers for the Kohn Laplacian on forms on the sphere in Cn
The unit sphere S in Cn is equipped with the tangential Cauchy–Riemann complex and the associated Laplacian □ b. We prove a Hörmander spectral multiplier theorem for □ b with critical index n- 1 / 2 , that is, half the topological dimension of S. Our proof is mainly based on representation theory and on a detailed analysis of the spaces of differential forms on S
The Hausdorff–Young inequality on Lie groups
We prove several results about the best constants in the Hausdorff–Young inequality for noncommutative groups. In particular, we establish a sharp local central version for compact Lie groups, and extend known results for the Heisenberg group. In addition, we prove a universal lower bound to the best constant for general Lie groups
Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres
A sharp Lp spectral multiplier theorem of Mihlin–Hörmander type is proved for a distinguished sub-Laplacian on quaternionic spheres. This is the first such result on compact sub-Riemannian manifolds where the horizontal space has corank greater than one. The proof hinges on the analysis of the quaternionic spherical harmonic decomposition, of which we present an elementary derivation
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