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1.
1IntroductionThe aim of the present paper is to construct an explicit expression of an heat kernel forthe Cayley Heisenberg group of order n.Hulanicki[1]and Gaveau[2]constructed the explicit expression of the heat kernel for theHeisenberg group by using p… 相似文献
2.
Guo-mao Wang 《高校应用数学学报(英文版)》2008,23(3):303-312
The purpose of this paper is to investigate the mean size formula of wavelet packets (wavelet subdivision tree) on Heisenberg group. The formula is given in terms of the p-norm joint spectral radius. The vector refinement equations on Heisenberg group and the subdivision tree on the Heisenberg group are discussed. The mean size formula of wavelet packets can be used to describe the asymptotic behavior of norm of the subdivision tree. 相似文献
3.
In this paper, sufficient and necessary conditions for the first order interpolation inequalities with weights on the Heisenberg
group are given. The necessity is discussed by polar coordinates changes of the Heisenberg group. Establishing a class of
Hardy type inequalities via a new representation formula for functions and Hardy-Sobolev type inequalities by interpolation,
we derive the sufficiency. Finally, sharp constants for Hardy type inequalities are determined. 相似文献
4.
Valentino Magnani 《Central European Journal of Mathematics》2006,4(1):82-109
We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence
of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measure. We explicitly compute this formula in some simple
examples and we present a lower semicontinuity result for the spherical Hausdorff measure with respect to the weak convergence
of currents. Another application is the proof of an intrinsic coarea formula for vector-valued mappings on the Heisenberg
group. 相似文献
5.
Sébastien Cartier 《Comptes Rendus Mathematique》2013,351(21-22):825-827
We give an immersion formula, the Sym–Bobenko formula, for minimal surfaces in the 3-dimensional Heisenberg space. Such a formula can be used to give a generalized Weierstrass type representation and construct explicit examples of minimal surfaces. 相似文献
6.
We investigate the octonion short-time linear canonical transform (OCSTLCT) in this paper. First, we propose the new definition of the OCSTLCT, and then several important properties of newly defined OCSTLCT, such as bounded, shift, modulation, time-frequency shift, inversion formula, and orthogonality relation, are derived based on the spectral representation of the octonion linear canonical transform (OCLCT). Second, by the Heisenberg uncertainty principle for the OCLCT and the orthogonality relation property for the OCSTLCT, the Heisenberg uncertainty principle for the OCSTLCT is established. Finally, we give an example of the OCSTLCT. 相似文献
7.
We build Wiener measure for the path space on the Heisenberg group by using of the heat kernel corresponding to the sub-Laplacian and give the definition of the Wiener integral. Then we give the Feynman-Kac formula. 相似文献
8.
We give a general setting for constructing a Weierstrass representation formula for simply connected minimal surfaces in a
Riemannian manifold. Then, we construct examples of minimal surfaces in the three dimensional Heisenberg group and in the
product of the hyperbolic plane with the real line.
Work partially supported by RAS, INdAM, FAPESP and CNPq 相似文献
9.
We derive the explicit fundamental solutions for a class of degenerate (or singular) one-parameter subelliptic differential operators on groups of Heisenberg (H) type. This extends the results of Kaplan of the sub-Laplacian on H-type groups, which in turn generalizes Folland's result on the Heisenberg group. As an application, we obtain a one-parameter representation formula for Sobolev functions of compact support on H-type groups. By choosing the parameter equal to the homogeneous dimension Q and using the Moser-Trudinger inequality for the convolutional type operator on stratified groups obtained in [18], we get the following theorem which gives the best constant for the Moser-Trudinger inequality for Sobolev functions in H-type groups. Let ${\Bbb G}We derive the explicit fundamental solutions for a class of degenerate (or singular) one-parameter subelliptic differential
operators on groups of Heisenberg (H) type. This extends the results of Kaplan of the sub-Laplacian on H-type groups, which
in turn generalizes Folland's result on the Heisenberg group. As an application, we obtain a one-parameter representation
formula for Sobolev functions of compact support on H-type groups. By choosing the parameter equal to the homogeneous dimension
Q and using the Moser-Trudinger inequality for the convolutional type operator on stratified groups obtained in [18], we get
the following theorem which gives the best constant for the Moser-Trudinger inequality for Sobolev functions in H-type groups.
Let ? be any group of Heisenberg type whose Lie algebra is g enerated by m left invariant vector fields and with a q-dimensional center. Let and
Then,
with A
Q
as the sharp constant, where ∇? denotes the subellitpic gradient on ?
This continues the research originated in our earlier study of the best constants in Moser-Trudinger inequalities and fundamental
solutions for one-parameter subelliptic operators on the Heisenberg group [18].
Received March 15, 2001, Accepted September 21, 2001 相似文献
10.
The authors define the Gauss map of surfaces in the three-dimensional Heisenberg group and give a representation formula for surfaces of prescribed mean curvature. Furthermore, a second order partial differential equation for the Gauss map is obtained, and it is shown that this equation is the complete integrability condition of the representation. 相似文献
11.
§1. IntroductionLetΩbearegularconeinRn,Φ:Cm×Cm→Cn=Rn+iRnanΩ-positiveHermitianmap.TheSiegeldomainDΩ,ΦoftypetwoinCn×CmisdefinedbyDΩ,Φ={(z,w)∈:Cn×Cm:Imz-Φ(w,w)∈Ω}(1)(see[6]).Specially,weassumethatn=m,Ω={t=(t1,t2,…,tn)∈Rn:ti>0,i=1,2,…,n},Φ(u,v)=u·v=(u1u… 相似文献
12.
《数学物理学报(B辑英文版)》2016,(3)
In this paper,we establish the partial Schauder estimates for the Kohn Laplace equation in the Heisenberg group based on the mean value theorem,the Taylor formula and a priori estimates for the derivatives of the Newton potential. 相似文献
13.
Wolfgang Staubach 《Journal d'Analyse Mathématique》2003,91(1):389-400
In this paper, we present an explicit calculation of the heat kernel, fundamental solution and Schwartz kernel of the resolvent
for the Heisenberg Laplacian using Wiener path integrals and their realizations via the Trotter product formula. This also
gives another derivation of mehler’s formula. 相似文献
14.
Klinger Andrew 《偏微分方程通讯》2013,38(11-12):2051-2060
The Heisenberg group gives rise to the simplest interesting example of a subellipticoperator. The hear kernel for this operator is known in terms of Fourier transforms. Here this hear kernel is derived in a simpleminded way from standard theroems in mathematical physics. A formula is given relating this kernel to the heat kernel of a magnetic field and ageneralization is given for similar geometries 相似文献
15.
In this paper cyclic one-cocycles of Heisenberg groups and some other Lie group are determined. The concept of almost Lie group of operators is introduced, and the trace formula is given by cyclicone cocyle on the Lie group. The Von Neumann theorem on Weyl commutation relation is generalized in certain case. 相似文献
16.
In this paper, we give an explicit formula for the Szegö kernel for (0, q) forms on the Heisenberg group Hn+1. 相似文献
17.
K. P. Kokhas´ 《Functional Analysis and Its Applications》2002,36(3):236-239
For a field F that is the direct limit of an increasing chain of finite fields, we describe the Bratteli diagram, the finite complex factor representations, the Plancherel formula, and the projective modules of the corresponding Heisenberg group. 相似文献
18.
We identify the short time asymptotics of the sub-Riemannian heat content for a smoothly bounded domain in the first Heisenberg group. Our asymptotic formula generalizes prior work by van den Berg–Le Gall and van den Berg–Gilkey to the sub-Riemannian context, and identifies the first few coe?cients in the sub-Riemannian heat content in terms of the horizontal perimeter and the total horizontal mean curvature of the boundary. The proof is probabilistic, and relies on a characterization of the heat content in terms of Brownian motion. 相似文献
19.
A curvature-type tensor invariant called para contact (pc) conformal curvature is defined on a paracontact manifold. It is
shown that a paracontact manifold is locally paracontact conformal to the hyperbolic Heisenberg group or to a hyperquadric
of neutral signature iff the pc conformal curvature vanishes. In the three dimensional case the corresponding result is achieved
through employing a certain symmetric (0,2) tensor. The well known result of Cartan–Chern–Moser giving necessary and sufficient
condition a CR-structure to be CR equivalent to a hyperquadric in
\mathbbCn+1{\mathbb{C}^{n+1}} is presented in-line with the paracontact case. An explicit formula for the regular part of a solution to the sub-ultrahyperbolic
Yamabe equation on the hyperbolic Heisenberg group is shown. 相似文献
20.
WenGuang Zhai 《中国科学A辑(英文版)》2009,52(5):857-874
In this paper we study the mean square of the error term in the Weyl’s law of an irrational (2l + 1)-dimensional Heisenberg manifold. An asymptotic formula is established.
This work was supported by National Natural Science Foundation of China (Grant No. 10771127) 相似文献