共查询到20条相似文献,搜索用时 15 毫秒
1.
Tai-Man Tang 《Acta Mathematica Hungarica》2000,89(3):247-251
For a class of real analytic functions on R, we give a condition for a function to be a quotient of two positive definite functions. 相似文献
2.
Positive Definite Functions and Operator Inequalities 总被引:1,自引:0,他引:1
We construct several examples of positive definite functions,and use the positive definite matrices arising from them toderive several inequalities for norms of operators. 1991 MathematicsSubject Classification 42A82, 47A63, 15A45, 15A60. 相似文献
3.
In this paper we develop an appropriate theory of positive definite functions on the complex plane from first principles and show some consequences of positive definiteness for meromorphic functions. 相似文献
4.
A characterization of bounded sets in Banach spaces in terms of asymptotic cones and the Hausdorff deviations of sets from them homothetic images is obtained. Similar results for generalizations of the notion of boundedness are presented. Boundedness criteria have previously been known only for recessively compact sets.
相似文献5.
Philippe Jaming Máté Matolcsi Szilárd G. Révész 《Journal of Fourier Analysis and Applications》2009,15(4):561-582
The aim of this paper is to investigate the cone of non-negative, radial, positive-definite functions in the set of continuous
functions on ℝ
d
. Elements of this cone admit a Choquet integral representation in terms of the extremals. The main feature of this article
is to characterize some large classes of such extremals. In particular, we show that there are many other extremals than the
Gaussians, thus disproving a conjecture of G. Choquet, and that no reasonable conjecture can be made on the full set of extremals.
The last feature of this article is to show that many characterizations of positive definite functions available in the literature
are actually particular cases of the Choquet integral representations we obtain. 相似文献
6.
讨论半群上条件正定函数的扩张问题.得到一个扩张定理.作为应用,得到有界扩张定理和Pontryagin空间上量子力学的一个基本定理. 相似文献
7.
We study the intimate relation of the continuation problem for hermitian positive definite functions with direct and inverse spectral problems for canonical systems and strings and with the extrapolation problem for second order stochastic processes. 相似文献
8.
Ulrich Hirth 《Journal of Theoretical Probability》2003,16(2):339-344
We prove that the set of exchangeable random totally ordered trees is a Bauer simplex whose extreme points are the generalized paint-box processes. The method is based on semigroups, analogous to Hirth and Ressel,(2, 3) and is readily also applied to inverse trees. 相似文献
9.
Hans Strauss 《Numerical Algorithms》2002,30(2):185-198
This paper deals with interpolation and approximation satisfying constraints. We consider approximation by conditionally positive definite functions in norms which are associated with the conditionally positive definite functions. The theory of reproducing kernels is used to transform the approximation problems to quadratic optimization problems. Then we can give the existence, characterization and uniqueness results for the solutions. The methods of optimization theory can be used in order to determine solutions. 相似文献
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E. A. Gorin 《Journal of Mathematical Sciences》2014,197(4):492-511
For the subject in question, the paper describes its connections that are close to the author’s interests with branches of functional analysis. The present survey may be suitable as a basis for a special course. 相似文献
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We derive a representation of orthogonal matrix polynomials on the real line as product of certain Schur complements and obtain matricial generalizations of well-known formulas for orthogonal scalar polynomials associated to a polynomial modified moment sequence. 相似文献
17.
Torben Maack Bisgaard 《Mathematische Nachrichten》2002,236(1):31-46
The problem of characterizing those semigroups of class ℳ︁ such that every positive definite function factors via the greatest C ‐separative ∗︁‐homomorphic image is shown to be equivalent to several other problems, including that of characterizing flat semigroups. If the latter could be solved then the problem of characterizing perfect semigroups would be reduced to characterizing quasi‐perfect semigroups. 相似文献
18.
If
converges for all
with all coefficients
, then the function
is positive definite on H×H for any inner product space H. Set K={k: a
k
>0}. We show that
is strictly positive definite if and only if K contains the index 0 plus an infinite number of even integers and an infinite number of odd integers. 相似文献
19.
研究了二元函数正定性的判别法,通过对二元函数定义和性质的讨论,得到了三个判别二元函数正定性的方法. 相似文献
20.
Let G be an additive subgroup of a normed space X. We say that a point is weakly separated (resp. -separated) from G if it can be separated from G by a continuous character (resp. by a continuous positive definite function). Let T : X → Y be a continuous linear operator. Consider the following conditions:
(ws) if , then x is weakly separated from G;
(ps) if , then x is -separated from G;
(wp) if Tx is -separated from T(G), then x is weakly separated from G.
By (resp. , ) we denote the class of operators T : X → Y which satisfy (ws) (resp. (ps), (wp)) for all and all subgroups G of X. The paper is an attempt to describe the above classes of operators for various Banach spaces X, Y. It is proved that if X, Y are Hilbert spaces, then is the class of Hilbert-Schmidt operators. It is also shown that if T is a Hilbert-to-Banach space operator with finite ℓ-norm, then .
相似文献