scholarly journals Tempered distributions on Heisenberg groups whose convolution with Schwartz class functions is Schwartz class

1981 ◽  
Vol 44 (3) ◽  
pp. 328-347 ◽  
Author(s):  
Lawrence Corwin
Keyword(s):  
Heisenberg Groups ◽  
Tempered Distributions ◽  
Schwartz Class

Fundamental Solutions of Kohn Sub-Laplacians on Anisotropic Heisenberg Groups and H-type Groups

2011 ◽  
Vol 54 (1) ◽  
pp. 126-140 ◽  
Author(s):  
Yongyang Jin ◽  
Genkai Zhang
Keyword(s):  
Fundamental Solutions ◽  
Meromorphic Continuation ◽  
Heisenberg Groups ◽  
Tempered Distributions

AbstractWe prove that the fundamental solutions of Kohn sub-LaplaciansΔ+iα∂t on the anisotropic Heisenberg groups are tempered distributions and have meromorphic continuation in α with simple poles. We compute the residues and find the partial fundamental solutions at the poles. We also find formulas for the fundamental solutions for some matrix-valued Kohn type sub-Laplacians on H-type groups.

Multilinear Stockwell transforms

2018 ◽  
Vol 13 (4) ◽  
pp. 35
Author(s):  
Viorel Catană
Keyword(s):  
Weight Function ◽  
Uncertainty Principle ◽  
Differential Operators ◽  
Tempered Distributions ◽  
Pseudo Differential Operators ◽  
Schwartz Class ◽  
Convolution Products ◽  
Decreasing Functions

The main aim of this paper is to introduce multilinear versions of the Stockwell transforms (also named S-transforms) by using the fact that S-transforms can be written as convolution products. Further on we extend the multilinear S-transforms from the Schwartz class of rapidly decreasing functions to the space of tempered distributions. In the sequel we give a relation between multilinear S-transforms and multilinear pseudo-differential operators. We also state and prove some boundedness results regarding multilinear S-transforms on the Lebegue’s spaces Lp(Rn) and also on the Hörmander’s spaces Bp,k(Rn), where p ≥ 1 and k is a temperate weight function. In the end, a weak uncertainty principle for multilinear S-transforms and for its adjoint is also given.

scholarly journals Counting and equidistribution in quaternionic Heisenberg groups

2021 ◽  
pp. 1-38
Author(s):  
JOUNI PARKKONEN ◽  
FRÉDÉRIC PAULIN
Keyword(s):  
Hyperbolic Geometry ◽  
Quaternion Algebra ◽  
Rational Points ◽  
Hyperbolic Spaces ◽  
Heisenberg Groups ◽  
Arithmetic Groups ◽  
Hermitian Forms ◽  
Dimension 2 ◽  
Counting Formula ◽  
The Relationship

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.

scholarly journals Quantum Heisenberg groups and sklyanin algebras

1994 ◽  
Vol 31 (3) ◽  
pp. 167-177 ◽  
Author(s):  
Nicol�s Andruskiewitsch ◽  
Jorge Devoto ◽  
Alejandro Tiraboschi
Keyword(s):  
Heisenberg Groups ◽  
Sklyanin Algebras

A representation of distributions supported on smooth hypersurfaces of Rn

1995 ◽  
Vol 117 (1) ◽  
pp. 153-160
Author(s):  
Kanghui Guo
Keyword(s):  
Gaussian Curvature ◽  
Dual Space ◽  
Smooth Hypersurface ◽  
Zero Gaussian Curvature ◽  
Schwartz Class ◽  
Image Position

Let S(Rn) be the space of Schwartz class functions. The dual space of S′(Rn), S(Rn), is called the temperate distributions. In this article, we call them distributions. For 1 ≤ p ≤ ∞, let FLp(Rn) = {f:∈ Lp(Rn)}, then we know that FLp(Rn) ⊂ S′(Rn), for 1 ≤ p ≤ ∞. Let U be open and bounded in Rn−1 and let M = {(x, ψ(x));x ∈ U} be a smooth hypersurface of Rn with non-zero Gaussian curvature. It is easy to see that any bounded measure σ on Rn−1 supported in U yields a distribution T in Rn, supported in M, given by the formula

scholarly journals Finite Heisenberg groups in quiver gauge theories

2006 ◽  
Vol 747 (3) ◽  
pp. 436-454 ◽  
Author(s):  
Benjamin A. Burrington ◽  
James T. Liu ◽  
Leopoldo A. Pando Zayas
Keyword(s):  
Gauge Theories ◽  
Heisenberg Groups

scholarly journals Wavelets in the generalized tempered distributions

1999 ◽  
Vol 23 (3) ◽  
pp. 529-538
Author(s):  
Byung Keun Sohn ◽  
Dae Hyeon Pahk
Keyword(s):  
Tempered Distributions
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