共查询到20条相似文献,搜索用时 343 毫秒
1.
Fabrizio Colombo Irene Sabadini Daniele C. Struppa 《Israel Journal of Mathematics》2009,171(1):385-403
In this paper we offer a new definition of monogenicity for functions defined on ℝ
n+1 with values in the Clifford algebra ℝ
n
following an idea inspired by the recent papers [6], [7]. This new class of monogenic functions contains the polynomials
(and, more in general, power series) with coefficients in the Clifford algebra ℝ
n
. We will prove a Cauchy integral formula as well as some of its consequences. Finally, we deal with the zeroes of some polynomials
and power series. 相似文献
2.
M. Aassila 《Rendiconti del Circolo Matematico di Palermo》2002,51(1):207-212
In this note we investigate the asymptotic behavior of solutions to the wave equation:u"-Δu+g(u')=0 in ℝnxℝ+. 相似文献
3.
Ricardo A. Sáenz 《Journal of Fourier Analysis and Applications》2012,18(2):240-265
In this paper we study the boundary limit properties of harmonic functions on ℝ+×K, the solutions u(t,x) to the Poisson equation
\frac?2 u?t2 + Du = 0,\frac{\partial^2 u}{\partial t^2} + \Delta u = 0, 相似文献
4.
Zhijian Wu 《Advances in Applied Clifford Algebras》1998,8(1):83-93
We decompose Lα2(ℝ+
n+1) into direct sum of closed subspaces which are isomorphic to the monogenic Bergman space. Application on commutators is also
discussed.
Research supported in part by the NSF Grant DMS-9622890 相似文献
5.
For a convex body K ⊂ ℝn and i ∈ {1, …, n − 1}, the function assigning to any i-dimensional subspace L of ℝn, the i-dimensional volume of the orthogonal projection of K to L, is called the i-th projection function of K. Let K, K
0 ⊂ ℝn be smooth convex bodies with boundaries of class C
2 and positive Gauss-Kronecker curvature and assume K
0 is centrally symmetric. Excluding two exceptional cases, (i, j) = (1, n − 1) and (i, j) = (n − 2, n − 1), we prove that K and K
0 are homothetic if their i-th and j-th projection functions are proportional. When K
0 is a Euclidean ball this shows that a convex body with C
2 boundary and positive Gauss-Kronecker with constant i-th and j-th projection functions is a Euclidean ball.
The second author was supported in part by the European Network PHD, FP6 Marie Curie Actions, RTN, Contract MCRN-511953. 相似文献
6.
The aim of this paper is to put the foundations of a new theory of functions, called holomorphic Cliffordian, which should
play an essential role in the generalization of holomorphic functions to higher dimensions. Let ℝ0,2m+1 be the Clifford algebra of ℝ2m+1 with a quadratic form of negative signature, be the usual operator for monogenic functions and Δ the ordinary Laplacian. The holomorphic Cliffordian functions are functionsf: ℝ2m+2 → ℝ0,2m+1, which are solutions ofDδ
m
f = 0.
Here, we will study polynomial and singular solutions of this equation, we will obtain integral representation formulas and
deduce the analogous of the Taylor and Laurent expansions for holomorphic Cliffordian functions.
In a following paper, we will put the foundations of the Cliffordian elliptic function theory. 相似文献
7.
WANG Meng CHEN Jiecheng & FAN Dashan Department of Mathematics Zhejiang University 《中国科学A辑(英文版)》2006,49(1):98-108
We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(P > 1) for Ω∈ e Llog L(Sn-1 × Sm-1) satisfying the cancellation condition. 相似文献
8.
Alexander Koldobsky 《Israel Journal of Mathematics》2011,185(1):277-292
We say that a random vector X = (X
1, …, X
n
) in ℝ
n
is an n-dimensional version of a random variable Y if, for any a ∈ ℝ
n
, the random variables Σa
i
X
i
and γ(a)Y are identically distributed, where γ: ℝ
n
→ [0,∞) is called the standard of X. An old problem is to characterize those functions γ that can appear as the standard of an n-dimensional version. In this paper, we prove the conjecture of Lisitsky that every standard must be the norm of a space that
embeds in L
0. This result is almost optimal, as the norm of any finite-dimensional subspace of L
p
with p ∈ (0, 2] is the standard of an n-dimensional version (p-stable random vector) by the classical result of P. Lèvy. An equivalent formulation is that if a function of the form f(‖ · ‖
K
) is positive definite on ℝ
n
, where K is an origin symmetric star body in ℝ
n
and f: ℝ → ℝ is an even continuous function, then either the space (ℝ
n
, ‖·‖
K
) embeds in L
0 or f is a constant function. Combined with known facts about embedding in L
0, this result leads to several generalizations of the solution of Schoenberg’s problem on positive definite functions. 相似文献
9.
I. V. Filimonova 《Journal of Mathematical Sciences》2007,143(4):3415-3428
One considers a semilinear parabolic equation u
t
= Lu − a(x)f(u) or an elliptic equation u
tt
+ Lu − a(x)f(u) = 0 in a semi-infinite cylinder Ω × ℝ+ with the nonlinear boundary condition
, where L is a uniformly elliptic divergent operator in a bounded domain Ω ∈ ℝn; a(x) and b(x) are nonnegative measurable functions in Ω. One studies the asymptotic behavior of solutions of such boundary-value problems
for t → ∞.
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 26, pp. 368–389, 2007. 相似文献
10.
Maria E. Schonbek 《Mathematische Annalen》2006,336(3):505-538
This paper considers the existence and large time behavior of solutions to the convection-diffusion equation u
t
−Δu+b(x)·∇(u|u|
q
−1)=f(x, t) in ℝ
n
×[0,∞), where f(x, t) is slowly decaying and q≥1+1/n (or in some particular cases q≥1). The initial condition u
0 is supposed to be in an appropriate L
p
space. Uniform and nonuniform decay of the solutions will be established depending on the data and the forcing term.This work is partially supported by an AMO Grant 相似文献
11.
G. I. Laptev 《Journal of Mathematical Sciences》2008,150(5):2384-2394
This paper deals with conditions for the existence of solutions of the equations
12.
We consider the parabolic Anderson problem ∂
t
u = κΔu + ξ(x)u on ℝ+×ℝ
d
with initial condition u(0,x) = 1. Here κ > 0 is a diffusion constant and ξ is a random homogeneous potential. We concentrate on the two important cases
of a Gaussian potential and a shot noise Poisson potential. Under some mild regularity assumptions, we derive the second-order
term of the almost sure asymptotics of u(t, 0) as t→∞.
Received: 26 July 1999 / Revised version: 6 April 2000 / Published online: 22 November 2000 相似文献
13.
R. Adamczak A. E. Litvak A. Pajor N. Tomczak-Jaegermann 《Constructive Approximation》2011,34(1):61-88
This paper considers compressed sensing matrices and neighborliness of a centrally symmetric convex polytope generated by
vectors ±X
1,…,±X
N
∈ℝ
n
, (N≥n). We introduce a class of random sampling matrices and show that they satisfy a restricted isometry property with overwhelming
probability. In particular, we prove that matrices with i.i.d. centered and variance 1 entries that satisfy uniformly a subexponential
tail inequality possess the restricted isometry property with overwhelming probability. We show that such “sensing” matrices
are valid for the exact reconstruction process of m-sparse vectors via ℓ
1 minimization with m≤Cn/log 2(cN/n). The class of sampling matrices we study includes the case of matrices with columns that are independent isotropic vectors
with log-concave densities. We deduce that if K⊂ℝ
n
is a convex body and X
1,…,X
N
∈K are i.i.d. random vectors uniformly distributed on K, then, with overwhelming probability, the symmetric convex hull of these points is an m-centrally-neighborly polytope with m∼n/log 2(cN/n). 相似文献
14.
Consider the system with perturbation g
k
∈ ℝ
n
and output z
k
= Cx
k
. Here, A
k
,A
k
(s) ∈ ℝ
n × n
, B
k
(1) ∈ ℝ
n × p
, B
k
(2) ∈ ℝ
n × m
, C ∈ ℝ
p × n
. We construct a special Lyapunov-Krasovskii functional in order to synthesize controls u
k
(1) and u
k
(2) for which the following properties are satisfied:
|
设为首页 | 免责声明 | 关于勤云 | 加入收藏 |
Copyright©北京勤云科技发展有限公司 京ICP备09084417号 |