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1.
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   

2.
通过Hermite矩阵的谱分解及一个改进的Young不等式,得到了关于正定矩阵的两个不等式,所得结果是对一些经典的矩阵不等式的进一步推广.最后,作为应用,给出了著名的Holder不等式和Minkowsi不等式的一种反向形式.  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.
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   

5.
本文得到实正定方阵行列式的几个不等式,改进了近期研究的一些结果.  相似文献   

6.
本文讨论了复正定矩阵行列式的估计式 ,修正了文 [2 ]的一些错误 ,得到了一些复正定矩阵行列式的不等式 .  相似文献   

7.
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   

8.
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   

9.
Let G be a locally compact commutative group and let g and h be positive definite functions on G, which are not identically zero. We show that continuity of gh? implies the existence of a character γ of Gd (the discrete version of G) such that γg and γh are continuous. As corollary we get a special case of a result of K. de Leeuw and I. Glicksberg concerning almost continuous group representations. In the second part of the paper we prove decomposition theorems for positive definite functions defined on a neighbourhood of the zero.  相似文献   

10.
11.
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   

12.
13.
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   

14.
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   

15.
本文指出文 [1 ]中的错误 ,并把文 [1 ]中关于复正定矩阵与正定 Hermite矩阵的行列式不等式推广到较为广泛的复矩阵类  相似文献   

16.
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   

17.
In the early 1930s, Wiener proved that if f(x) is a strictlypositive periodic function whose Fourier series is absolutelyconvergent, then the Fourier series of g(x)=1/f(x) is also absolutelyconvergent [8, pp. 10–14]. This phenomenon can be easilyunderstood nowadays using Banach algebra techniques (see, forexample, [4, pp. 202–203]). In fact, these techniquesallow us to study the absolute convergence of g(x)=F(f(x)),where F is holomorphic in an open subset of C that containsthe range of f(x) (for xR). In this context, Wiener's originalproblem corresponds to the choice F(z)=1/z. In this work we want to analyse the constraints on the simultaneousrate of vanishing of the Fourier coefficients f(n) and (n) asn. We shall focus on g=1/f, but we shall also study the generalcase g=F(f). In either case, there are obviously no constraintswhen f is a constant function. Although this problem does not seem to be directly related touncertainty inequalities for the Fourier Transform, we observethat there are some analogies, both in the nature of the resultsand in the proof techniques. The general fact with which weare dealing is that f(n) and (n) cannot vanish too quickly atthe same time as n, unless f(x) is constant. The general factthat underlies uncertainty inequalities is that a non-periodicfunction (x) and its Fourier Transform circ;(u) cannot vanishtoo quickly at the same time as x and u, unless (x) is zero(almost everywhere). For a simple introduction to some aspectsof uncertainty inequalities, see [5]; for a thorough and recentintroduction to this vast subject, see [3]. 1991 MathematicsSubject Classification 42A05, 42A16, 42A99.  相似文献   

18.
Strictly Positive Definite Functions on a Real Inner Product Space   总被引:1,自引:0,他引:1  
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.
Rabaoui  M. 《Mathematical Notes》2019,106(5-6):966-969
Mathematical Notes - In this paper, using a Bochner-type theorem, we establish a characterization of strictly positive definite functions on the topological direct limit space D∞ of real...  相似文献   

20.
The nth cyclic function is defined by

We prove that if k is an integer with 1kn−1, then

holds for all positive real numbers x with the best possible constantsα=1 and β= 2n-k over n.  相似文献   

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