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1.
In this paper we consider an extremum problem for even periodic functions having small intervals as their supports and subject
to restrictions on the sum of the absolute values of their Fourier coefficients.
Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 323–332, September, 1996.
We wish to express our gratitude to S. B. Stechkin for his interest in our work.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00378, and the work of the
first and second authors also by the International Science Foundation under grant No. MC5300. 相似文献
2.
O. V. Besov 《Mathematical Notes》1998,64(3):303-315
We obtain sufficient conditions on a domainG ⊂ ℝn for functions defined onG to be extendable by zero to the entire space ℝn with smoothness preserved in an integral norm.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 351–365, September, 1998.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00243 and by program “Leading
Science Schools” under grant No. 96-15-96102. 相似文献
3.
Growth behavior of a class of merit functions for the nonlinear complementarity problem 总被引:3,自引:0,他引:3
P. Tseng 《Journal of Optimization Theory and Applications》1996,89(1):17-37
When the nonlinear complementarity problem is reformulated as that of finding the zero of a self-mapping, the norm of the selfmapping serves naturally as a merit function for the problem. We study the growth behavior of such a merit function. In particular, we show that, for the linear complementarity problem, whether the merit function is coercive is intimately related to whether the underlying matrix is aP-matrix or a nondegenerate matrix or anR
o-matrix. We also show that, for the more popular choices of the merit function, the merit function is bounded below by the norm of the natural residual raised to a positive integral power. Thus, if the norm of the natural residual has positive order of growth, then so does the merit function.This work was partially supported by the National Science Foundation Grant No. CCR-93-11621.The author thanks Dr. Christian Kanzow for his many helpful comments on a preliminary version of this paper. He also thanks the referees for their helpful suggestions. 相似文献
4.
D. V. Prokhorov 《Mathematical Notes》1997,61(5):609-613
We solve the maximal value problem for the functional
in the class of functionsf(z)=z+a
2z2+… that are holomorphic and univalent in the unit disk and satisfy the inequality |f(z)|<M. We prove that the Pick functions are extremal for this problem for sufficiently largeM whenever the set of indicesk
1,…,km contains an even number.
Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 728–733, May, 1997.
Translated by S. S. Anisov 相似文献
5.
S. S. Volosivets 《Mathematical Notes》1997,62(3):306-313
In this paper the best polynomial approximation in terms of the system of Faber-Schauder functions in the spaceC
p
[0, 1] is studied. The constant in the estimate of Jackson’s inequality for the best approximation in the metric ofC
p
[0, 1] and the estimate of the modulus of continuity ω1−1/p
are refined.
Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 363–371, September, 1997.
Translated by N. K. Kulman 相似文献
6.
Lian Zhong YANG Hong Xun YI 《数学学报(英文版)》2007,23(8):1405-1412
In this paper, we prove several results concerning meromorphic functions f and g of hyperorder less than one such that f^(j) and g^(j) have the same zeros and poles for j=0, 1, 2. We provide some examples to show that our results are sharp. 相似文献
7.
We discuss zeta extensions in the sense of Kurokawa and Wakayama, Proc. Japan Acad. 2002, for constructing new zeta functions from a given zeta function. This notion appeared when we introduced higher zeta functions such as higher Riemann zeta functions in Kurokawa et al., Kyushu Univ. Preprint, 2003, and a higher Selberg zeta functions in Kurokawa and Wakayama, Comm. Math. Phys., 2004. In this article, we first recall some explicit examples of such zeta extensions and give a conjecture about functional equations satisfied by higher zeta functions. We devote the second part to making a detailed study of the double sine functions which are treated in a framework of the zeta extensions.Mathematics Subject Classification (2000) 11M36.Partially supported by Grant-in-Aid for Scientific Research (B) No. 15340012, and by Grant-in-Aid for Exploratory Research No. 13874004. This is based on the talk at The 2002 Twente Conference on Lie Groups 16–18 Dec. University of Twente, Enschede, The Netherlands. 相似文献
8.
Yu. A. Dubinskii 《Mathematical Notes》1998,64(1):38-48
The problem of continuing a function from the unit circle to the unit disk so that the continuation has the least deviation from the Sobolev subspace of analytic functions is considered. A mathematical model of this problem is constructed. It is proved that the problem is well-posed.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 45–57, July, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00621. 相似文献
9.
Based on radial basis functions approximation, we develop in this paper a new com-putational algorithm for numerical differentiation.
Under an a priori and an a posteriori choice rules for the regularization parameter, we also give a proof on the convergence error estimate in reconstructing the
unknown partial derivatives from scattered noisy data in multi-dimension. Numerical examples verify that the proposed regularization
strategy with the a posteriori choice rule is effective and stable to solve the numerical differential problem.
*The work described in this paper was partially supported by a grant from CityU (Project No. 7001646) and partially supported
by the National Natural Science Foundation of China (No. 10571079). 相似文献
10.
It is proved that the Bergman type operatorT, is a bounded projection from the pluriharmonic Bergman spaceL
p
(B)∩h(B) onto Bergman spaceL
p
(B) ∩
H(B) for 0p 1 ands (p1-1)(n+1). As an application it is shown that the Gleason’s problem can be solved in Bergman space LP(B)∩H(B) for 0p 1.
Project supported by the National Natural Science Foundation of China (Grant No. 19871081) and the Doctoral Program Foundation
of the State Education Commission of China. 相似文献
11.
Let be the class of functions which are analytic in the unit disk . Let C(r) be the closed curve that is the image of the circle |z|=r < 1 under the mapping w = f(z), L(r) the length of C(r), and let A(r) be the area enclosed by the curve C(r). In 1968 D. K. Thomas shown that if , f is starlike with respect to the origin, and for 0≤r < 1, A(r) < A, an absolute constant, then Later, in 1969 Nunokawa has shown that if f is convex univalent, then This paper is devoted to obtaining a related correspondence between f(z) and L(r) for the case when f is univalent. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
12.
A. V. Niukkanen 《Mathematical Notes》2000,67(4):487-494
It is shown that the formulas of operator factorization of hypergeometric functions obtained in the author’s previous works
can be extended to hypergeometric series of the most general form. This generalization does not make the technical apparatus
of the factorization method more complicated. As an example illustrating the practical effectiveness of the formulas obtained
in the paper, we analyze transformation properties of the Horn seriesG
3, whose structure is typical for general hypergeometric functions. It is shown that Erdélyi’s transformation formula relating
the seriesG
3 to the Appell functionF
2, contains erroneous expressions in the arguments ofG
3. The correct analog of Erdélyi’s formula is found, and some new transformations of the seriesG
3 are presented.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 573–581, April, 2000. 相似文献
13.
B. R. Frenkin 《Mathematical Notes》2000,67(1):112-118
Two topological variants of the minimax theorem are proved with no restrictions on one of the spaces except for those related
to the function under consideration. The conditions concerning the behavior of the function deal only with the interval between
the maximin and minimax. As corollaries, we obtain the well-known theorems of Sion and Hoang-Tui on quasiconvex-quasiconcave
semicontinuous functions. The scheme of arguments goes back to the Hahn-Banach theorem and the separating hyperplane theorem.
It is shown how this scheme can be explicitly realized in the proof of the Hahn-Banach theorem.
Translated fromMaternaticheskie Zametki, Vol. 67, No. 1, pp. 141–149, January, 2000. 相似文献
14.
We show that the local trigonometric bases introduced by Malvar, Coifman and Meyer constitute bases, but not unconditional
bases, for Lp(ℝ) with 1<p<∞, p≠2. In addition, we characterize the functions in Lp(ℝ) for 1<p<∞ in terms of their local trigonometric basis coefficients.
Dedicated to Dr. Charles A. Micchelli for his 60th birthday
Mathematics subject classification (2000) 42C15.
Supported by Prof. Y. Xu under his grant in program of “One Hundred Distinguished Chinese Scientists” of the Chinese Academy
of Sciences, the National Natural Science Foundation of China (No. 10371122), and the second author is supported by Tianyuan
Fund for Mathematics (No. A0324648). 相似文献
15.
There are basic equivalent assertions known for operator monotone functions and operator convex functions in two papers by Hansen and Pedersen. In this note we consider their results as correlation problem between two sequences of matrix n-monotone functions and matrix n-convex functions, and we focus the following three assertions at each label n among them:
- (i) f(0)0 and f is n-convex in [0,α),
- (ii) For each matrix a with its spectrum in [0,α) and a contraction c in the matrix algebra Mn,f(cac)cf(a)c,