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1.
Evsey Dyn'kin 《Journal of Approximation Theory》1997,91(3):349-367
A new hyperbolic area estimate for the level sets of finite Blaschke products is presented. The following inversion of the usual Sobolev embedding theorem is proved:
Hereris a rational function of degreenwith poles outside
. This estimate implies a new inverse theorem for rational approximation of analytic functions with respect to areaLpnorm. 相似文献
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2.
I. Scherbak 《Geometric And Functional Analysis》2002,12(6):1365-1380
A rational function is the ratio of two complex polynomials in one variable without common roots. Its degree is the maximum of the degrees of the numerator and the denominator. Rational functions belong to the same class if one turns into the other by postcomposition with a linear-fractional transformation. We give an explicit formula for the number of classes having a given degree d and given multiplicities m1,..., mn of given n critical points, for generic positions of the critical points. This number is the multiplicity of the irreducible sl2 representation with highest weight
in the tensor product of the irreducible sl2 representations with highest weights
The classes are labeled by the orbits of critical points of a remarkable symmetric function which first appeared in the XIX century in studies of Fuchsian differential equations, and then in the XX century in the theory of KZ equations. 相似文献
3.
Rational interpolants, some of the poles of which are left free, are used to approximate the transfer functions of a large class of possibly unstable infinite-dimensional control systems. The free poles are used to detect the singularities of the transfer function which are responsible for the instability of the system. 相似文献
4.
Ukrainian Mathematical Journal - For a rational function r(z)?=?p(z)/H(z) all zeros of which are in |z|?≤?1, it is known that $$ left|r^{prime }(z)right|ge... 相似文献
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Arnold Neumaier 《Journal of Global Optimization》2003,25(2):175-181
A family of multivariate rational functions is constructed. It has strong local minimizers with prescribed function values at prescribed positions. While there might be additional local minima, such minima cannot be global. A second family of multivariate rational functions is given, having prescribed global minimizers and prescribed interpolating data. 相似文献
7.
Markov- and Bernstein-Type Inequalities for Polynomials with Restricted Coefficients 总被引:1,自引:0,他引:1
The Markov-type inequality
is proved for all polynomials of degree at most n with coefficients from {-1,0,1} with an absolute constant c. Here ·[0,1] denotes the supremum norm on [0,1]. The Bernstein-type inequality
is shown for every polynomial p of the form
The inequality
is also proved for every analytic function p on the open unit disk D that satisfies the growth condition
相似文献
8.
We extend some results of Giroux and Rahman (Trans. Amer. Math. Soc.193(1974), 67–98) for Bernstein-type inequalities on the unit circle for polynomials with a prescribed zero atz=1 to those for rational functions. These results improve the Bernstein-type inequalities for rational functions. The sharpness of these inequalities is also established. Our approach makes use of the Malmquist–Walsh system of orthogonal rational functions on the unit circle associated with the Lebesgue measure. 相似文献
9.
G. Min 《Acta Mathematica Hungarica》1999,82(1-2):11-20
We study Turán-type inequalities for the derivatives of rational functions, whose zeros are all real and lie inside [-1,1] but whose poles are outside (-1,1), in the supremum- and L2-norms respectively. We generalize several well-known results for classical polynomials. We also obtain a sharp L2 Bernstein-type inequality for the rational system with prescribed poles. 相似文献
10.
T. Nishishiraho 《Acta Mathematica Hungarica》1999,84(1-2):149-158
A sequence of Bernstein-type operators for vector-valued functions is provided and its uniform convergence is considered by making use of a theorem of Korovkin type under certain requirements. 相似文献
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Mathematical Notes - For rational functions with prescribed poles lying outside the unit circle $$|z|=1$$ , sharp inequalities are established at points $$z$$ , $$|z|=1$$ . In contrast to known... 相似文献
13.
We obtain explicit upper estimates in direct inequalities with respect to the usual sup-norm distance for Bernstein-type operators. Our approach combines analytical and probabilistic techniques based on representations of the operators in terms of stochastic processes. We illustrate our results by considering some classical families of operators, such as Weierstrass, Szàsz, and Bernstein operators. 相似文献
14.
Let Pn be the collection of all polynomials of degree at mostn with real coefficients. A subtle Bernstein-type extremal problemis solved by establishing the inequality
for all , and m= 1, 2, ..., where c is an absolute constant and
Some related inequalities and direct and inversetheorems about the approximation by elements of in Lq (R) are also discussed. 2000 Mathematics SubjectClassification 41A17 (primary). 相似文献
15.
设Γ∈C(1,α),α>0.G是复平面上以Γ为边界的有界单连通区域.本文考虑了极点位于G外部,以广义Faber-Dzrbasjan有理函数的零点为插值结点的Lagrange插值有理函数序列对A(G)和Eq(G)(1<q<+∞)中函数的一致逼近和平均逼近阶的估计. 相似文献
16.
Siberian Mathematical Journal - We establish some inequalities for the modulus of the derivative of rational functions of Bernstein and Turán type in the sup-norm on the unit disk in the... 相似文献
17.
Let k 1 and
be a system of rational functions forming a strongly linearly independent set over a finite field
. Let
be arbitrarily prescribed elements. We prove that for all sufficiently large extensions
, there is an element
of prescribed order such that
is the relative trace map from
onto
We give some applications to BCH codes, finite field arithmetic and ordered orthogonal arrays. We also solve a question of Helleseth et~al. (Hypercubic 4 and 5-designs from Double-Error-Correcting codes, Des. Codes. Cryptgr. 28(2003). pp. 265–282) completely.classification 11T30, 11G20, 05B15 相似文献
18.
We consider real functions on [a, b] for which some derivatives have constant sign. For these functions we obtain Popoviciu and Favard-Berwald type inequalities as well as converse Holder inequalities. 相似文献
19.
S. J. Gardiner 《Constructive Approximation》2001,17(1):139-146
Let Ω be a domain in the extended complex plane such that ∞∈Ω . Further, let K= C / Ω and, for each n , let Q
n
be a monic polynomial of degree n with all its zeros in K . This paper is concerned with whether (Q
n
) can be chosen so that, if f is any holomorphic function on Ω and P
n
is the polynomial part of the Laurent expansion of Q
n
f at ∞ , then (P
n
/Q
n
) converges to f locally uniformly on Ω . It is shown that such a sequence (Q
n
) can be chosen if and only if either K has zero logarithmic capacity or Ω is regular.
January 21, 1999. Date accepted: August 17, 1999. 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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