共查询到20条相似文献,搜索用时 15 毫秒
1.
Joachim Zacharias 《Proceedings of the American Mathematical Society》2006,134(7):1909-1916
Recently J.Roe considered the question of whether for a discrete group the reduced group -algebra is the fixed point algebra of Ad acting on the uniform Roe algebra . is said to have the invariant translation approximation property in this case. We consider a slight generalization of this property which, for exact , is equivalent to the operator space approximation property of . We also give a new characterization of exactness and a short proof of the equivalence of exactness of and exactness of for discrete groups.
2.
Let G be a bounded N-connected domain, the boundary of which consists of closed analytic Jordan curves. We assume that 0G. For any nonnegative integers n and m, denote by
n,m
the class of all meromorphic functions on G that can be represented in the form h=p/qz
m
, where p belongs to the Smirnov class E
(G), q is a polynomial of degree at most n, q0. Theorems giving necessary and sufficient conditions for a function belonging to the class
n,m
to be an element of best approximation to a continuous function f on in the space L
() by functions in the class
n,m
are proved. Some questions concerning orthogonal polynomials and the theory of Hankel operators are also considered. 相似文献
3.
Qingzhai Fan 《Israel Journal of Mathematics》2013,195(2):545-563
We show that the Riesz interpolation property of the K 0-monoid of C*-algebras in the class Ω is inherited by simple unital C*-algebras in the class TAΩ, and the property of being an admissible target algebras of finite type in the class of Ω is inherited by unital C*-algebras in the class TAΩ. 相似文献
4.
This paper contains some theorems related to the best approximation ρn(f;E) to a function f in the uniform metric on a compact set by rational functions of degree at most n. We obtain results characterizing the relationship between ρn(f;K) and ρn(f;E) in the case when complements of compact sets K and E are connected, K is a subset of the interior Ω of E, and f is analytic in Ω and continuous on E. 相似文献
5.
We consider 3-monotone approximation by piecewise polynomials with prescribed knots. A general theorem is proved, which reduces the problem of 3-monotone uniform approximation of a 3-monotone function, to convex local L1 approximation of the derivative of the function. As the corollary we obtain Jackson-type estimates on the degree of 3-monotone approximation by piecewise polynomials with prescribed knots. Such estimates are well known for monotone and convex approximation, and to the contrary, they in general are not valid for higher orders of monotonicity. Also we show that any convex piecewise polynomial can be modified to be, in addition, interpolatory, while still preserving the degree of the uniform approximation. Alternatively, we show that we may smooth the approximating piecewise polynomials to be twice continuously differentiable, while still being 3-monotone and still keeping the same degree of approximation. 相似文献
6.
Zhijian Qiu 《数学学报(英文版)》2009,25(7):1217-1222
Let G be an open subset in the extended complex plane and let A(G) denote the algebra of all functions analytic on G and continuous on G. We call a domain multi-nicely connected if there is a circular domain W and a conformal map ~ from W onto G such that the boundary value function of φ is univalent almost everywhere with respect to the arclength on aW. Suppose that every component of G is finitely connected and none of the components of G have single point boundary components. We show that for every bounded analytic function on G to be the pointwise limit of a bounded sequence of functions in A(G), it is necessary and sufficient that each component of G is multi-nicely connected and the harmonic measures of G are mutually singular. This generalizes the corresponding result of Davie for the case when the components of G are simply connected. 相似文献
7.
N. Hussain 《分析论及其应用》2006,22(1):72-80
We extend the concept of R-subcommuting maps due to Shahzad[17,18] to the case of non-starshaped domain and obtain a common fixed point result for this class of maps on non-starshaped domain in the setup of p-normed spaces. As applications, we establish noncommutative versions of various best approximation results for generalized I-nonexpansive maps on non-starshaped domain. Our results unify and extend that of Al-Thagafi, Dotson, Habiniak,Jungck and Sessa, Latif, Sahab, Khan and Sessa and Shahzad. 相似文献
8.
T. Zaimi 《Acta Mathematica Hungarica》2002,96(4):309-325
Let 1<q<2 be a real number, m≥1 be a rational integer and lm(q)={|P(q)|,P∈Z[X],P(q)≠0,H(P)≤m}, where Z[X] denotes the set of polynomials P with rational integer coefficients and H(P)
is the height of P. The value of lm(q) was determined for many particular Pisot numbers ([3] and [7]). In this paper we determine the infimum and the supremum
of the numbers lm(q) for any fixed m. We also determine the greatest limit point for the case m=1.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
We consider approximation problems for a special space of d variate functions. We show that the problems have small number of active variables, as it has been postulated in the past using concentration of measure arguments. We also show that, depending on the norm for measuring the error, the problems are strongly polynomially or quasi-polynomially tractable even in the model of computation where functional evaluations have the cost exponential in the number of active variables. 相似文献
10.
On weighted polynomial approximation with monotone weights 总被引:1,自引:0,他引:1
Alexander Borichev 《Proceedings of the American Mathematical Society》2000,128(12):3613-3619
We construct an even weight monotone on the right half line such that the logarithmic integral of the largest -convex minorant of converges and the polynomials are dense in . 相似文献
11.
Lucyna Rempulska Mariola Skorupka 《分析论及其应用》2006,22(2):172-182
We introduce modified Post-Widder operators in polynomial weighted spaces of differentiable functions and we study strong approximation for them. 相似文献
12.
Ju Myung Kim 《Journal of Mathematical Analysis and Applications》2006,324(1):721-727
It is shown that for the separable dual X∗ of a Banach space X, if X∗ has the weak approximation property, then X∗ has the metric weak approximation property. We introduce the properties W∗D and MW∗D for Banach spaces. Suppose that M is a closed subspace of a Banach space X such that M⊥ is complemented in the dual space X∗, where for all m∈M}. Then it is shown that if a Banach space X has the weak approximation property and W∗D (respectively, metric weak approximation property and MW∗D), then M has the weak approximation property (respectively, bounded weak approximation property). 相似文献
13.
LetZ be a compact set of the real space with at leastn + 2 points;f,h1,h2:Z continuous functions,h1,h2 strictly positive andP(x,z),x(x
0,...,x
n
)
n+1,z , a polynomial of degree at mostn. Consider a feasible setM {x
n+1z Z, –h
2(z) P(x, z)–f(z)h
1(z)}. Here it is proved the null vector 0 of
n+1 belongs to the compact convex hull of the gradients ± (1,z,...,z
n
), wherez Z are the index points in which the constraint functions are active for a givenx* M, if and only ifM is a singleton.This work was partially supported by CONACYT-MEXICO. 相似文献
14.
We investigate the approximation by manifolds n() generated by linear combinations of n radial basis functions on Rd of the form (|–a|), where is the thin-plate spline type function. We obtain exact asymptotic estimates for the approximation of Sobolev classes Wr(Bd) in the space L(Bd) on the unit ball Bd.
AMS subject classification 41A25, 41A63, 65D07, 41A15 相似文献
15.
Tracial Limit of C^*-algebras 总被引:4,自引:0,他引:4
ShanWenHU HuaXinLIN YiFengXUE 《数学学报(英文版)》2003,19(3):535-556
A new limit of C^*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C^*-algebra A is a tracial limit of C^*-algebras in Z-(k) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits. 相似文献
16.
17.
We show that on some open sets, more general than balls, Runge approximation is possible in certain Banach spaces, and also in certain complex Banach manifolds. We also show that there is an entire holomorphic curve in Hilbert space on which there is a bounded holomorphic function on the trace of a ball that has no bounded holomorphic extension to even a smaller concentric ball. Using the same technique we also prove that a form of Runge approximation better than an error function is not always possible. 相似文献
18.
We show that the strong approximation property (strong AP) (respectively, strong CAP) and the weak bounded approximation property (respectively, weak BCAP) are equivalent for every Banach space. This gives a negative answer to Oja's conjecture. As a consequence, we show that each of the spaces c0 and ?1 has a subspace which has the AP but fails to have the strong AP. 相似文献
19.
YEMAODONG 《高校应用数学学报(英文版)》1998,13(1):117-122
In this paper a representation for linear polynomial projection is given. Then it isshown that the near minimax approximation is equivalant to a problem of the best approxima-tion of hivariste functions. And some properties for near minimax are obtained. 相似文献
20.
When G is a finite dimensional Haar subspace of C(X,Rk), the vector-valued continuous functions (including complex-valued functions when k is 2) from a finite set X to Euclidean k-dimensional space, it is well-known that at any function f in C(X,Rk) the best approximation operator satisfies the strong unicity condition of order 2 and a Lipschitz (Hőlder) condition of order . This note shows that in fact the best approximation operator satisfies the usual Lipschitz condition of order 1. 相似文献