共查询到20条相似文献,搜索用时 15 毫秒
2.
给出了三次Hyers—Ulam—Rassias型泛函方程的一种新表示方法af(x+ay)-f(ax+y)=(a(a~2-1))/2[f(x+y)+f(x-y)]+(a~4-1)f(y)-2a(a~2-1)f(x)其中a为整数且a≠0,土1.关于9个三次泛函方程给出等价性证明。对Banach空间三次方程的稳定性问题给予讨论。 相似文献
3.
Let G be an Abelian group and let ρ : G×G→[0,∞) be a metric on GLet E be a normed spaceWe prove that under some conditions if f : G→E is an odd function and Cx : G→E defined by Cx(y) := 2 f(x + y) +2 f(x-y) + 12 f(x)-f(2x + y)-f(2x-y)is a cubic function for all x∈G, then there exists a cubic function C : G→E such that f-C is LipschitzMoreover, we investigate the stability of cubic functional equation2 f(x + y) + 2 f(x-y) + 12 f(x)-f(2x + y)-f(2x-y) = 0 on Lipschitz spaces. 相似文献
4.
5.
Our randomized preprocessing enables pivoting-free and orthogonalization-free solution of homogeneous linear systems of equations. In the case of Toeplitz inputs, we decrease the estimated solution time from quadratic to nearly linear, and our tests show dramatic decrease of the CPU time as well. We prove numerical stability of our approach and extend it to solving nonsingular linear systems, inversion and generalized (Moore-Penrose) inversion of general and structured matrices by means of Newton’s iteration, approximation of a matrix by a nearby matrix that has a smaller rank or a smaller displacement rank, matrix eigen-solving, and root-finding for polynomial and secular equations and for polynomial systems of equations. Some by-products and extensions of our study can be of independent technical intersest, e.g., our extensions of the Sherman-Morrison-Woodbury formula for matrix inversion, our estimates for the condition number of randomized matrix products, and preprocessing via augmentation. 相似文献
6.
7.
Banach空间中线性算子的齐性广义逆 总被引:9,自引:0,他引:9
本文首先在Banach空间内引进拟线性投影算子的概念,由此给出Banach空 间内线性算子的齐性广义逆的统一定义。齐性广义逆包含线性广义逆、单值度量广义 逆.本文证得齐性广义逆存在的充分必要条件. 相似文献
8.
HongZeLI RichardJ.MCINTOSH 《数学学报(英文版)》2004,20(5):837-850
In this paper, we consider the simultaneous representation of pairs of integers as linear combinations in three prime variables and obtain a related numerical bound. 相似文献
9.
Let G be a compact group, H a closed subgroup of G and let m be the normalized G-invariant measure on the homogeneous space G / H obtained from Weil’s formula. In this article, for a given Young function \(\varphi \), we give a new class of Banach convolution algebras on homogeneous spaces of compact groups by introducing a convolution and an involution on the Orlicz space \(L^\varphi (G/H, m)\). Finally, a class of linear representations of this class of Banach convolution algebras is presented. 相似文献
10.
A.-M. LI H. L. LIU A. SCHWENK-SCHELLSCHMIDT U. SIMON C. P. WANG 《Geometriae Dedicata》1997,66(2):203-221
We introduce the concept of a relative Tchebychev hypersurface which extends that of affine spheres in equiaffine geometry and also that of centroaffine Tchebychev hypersurfaces and give partial local and global classifications for this new class. Our tools concern a new operator and interesting properties of the traceless part of the cubic form. 相似文献
11.
研究了一类高阶齐次线性微分方程解的零点收敛指数,并得到当方程的系数A_0为整函数,其泰勒展式为缺项级数,并且A_0起控制作用时,方程f~((k))+A_(k-2)f~((k-2))+…+A_1f′+A_0f=0的任意两个线性无关解f_1,f_2满足max{λ(f_1),λ(f_2)}=∞,其中λ(f)表示亚纯函数.f的零点收敛指数. 相似文献
12.
Mathematical Notes - 相似文献
13.
14.
15.
Cubic Splines on Curved Spaces 总被引:5,自引:0,他引:5
NOAKES LYLE; HEINZINGER GREG; PADEN BRAD 《IMA Journal of Mathematical Control and Information》1989,6(4):465-473
We consider a second-order problem in the calculus of variations,with an application to robotics in mind. The analysis is carriedout on a general Riemannian manifold M and then specializedto the case where M is the Lie group SO(3) of rotations in R3.For SO(3), the Euler-Lagrange equations reduce to interestingnonlinear systems of ordinary differential equations in R3. 相似文献
16.
给出了齐型空间上Lipschitz函数空间的两个新的等价范数,证明了Lipschitz函数满足与BMO函数类似的Joho-Nirenberg型不等式. 相似文献
17.
Stephan Dahlke Gabriele Steidl Gerd Teschke 《Journal of Fourier Analysis and Applications》2004,10(5):507-539
This article is concerned with frame constructions on domains and manifolds. The
starting point is a unitary group representation which is square integrable modulo a suitable
subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized
coorbit spaces can be defined by collecting all functions for which this wavelet transform
is contained in a weighted Lp-space. Moreover, we show that a judicious discretization of the
representation leads to an atomic decomposition and to Banach frames for these coorbit spaces. 相似文献
18.
The structure of the set of E-functions satisfying second-order homogeneous linear differential equations with coefficients from $\mathbb{C}(z)$ is described. 相似文献
19.
20.
This paper is a short research announcement of the results obtained in [BD], which will appear soon. 相似文献