共查询到20条相似文献,搜索用时 15 毫秒
1.
T. A. Zhereb’eva 《Moscow University Mathematics Bulletin》2010,65(1):16-22
A problem of uniqueness for series over multiplicative systems of functions and for multiplicative transforms is considered.
It is shown that each set of uniqueness for a multiplicative transform is specified by a countable collection of sets of uniqueness
for series over the corresponding multiplicative system of functions. Each set of uniqueness for a series over a multiplicative
system of functions is a portion on [0, 1) of some set of uniqueness for the corresponding multiplicative transform. 相似文献
2.
T. A. Zhereb’eva 《Moscow University Mathematics Bulletin》2007,62(5):181-185
A problem of uniqueness for multiple Walsh series is considered. A class of uniqueness sets for double Walsh series is obtained, this class contains known classes of uniqueness sets. 相似文献
3.
M. G. Plotnikov 《Mathematical Notes》2007,81(1-2):234-246
We study uniqueness sets for multiple Walsh series under ρ-regular (or bounded) convergence in rectangles. We prove that a countable set is a uniqueness set for such a series under this convergence. We construct a class of perfect uniqueness sets for multiple Walsh series under this convergence. We show that the notion of index of a perfect set does not solve the problem of whether this set belongs to the class of uniqueness sets. We note that the results of this paper remain valid for several rearranged multiple Walsh series. 相似文献
4.
N. N. Kholshchevnikova 《Mathematical Notes》2000,67(5):657-664
The properties of families of subsets of topological spaces that make it possible to separate out the common core of the proofs
of theorems on unions of sets of uniqueness for series in various systems of functions are considered. As a consequence of
the results obtained, it is proved, in particular, that the countable union of closed sets of uniqueness for the trigonometric
series is a set of uniqueness for the Abel-Poisson summation method.
Translated fromMatematicheskie Zametki, Vol. 67, No. 5, pp. 778–787, May, 2000. 相似文献
5.
Ta Thi Hoai An Julie Tzu-Yueh Wang 《Transactions of the American Mathematical Society》2007,359(3):937-964
We study unique range sets and uniqueness polynomials for algebraic functions on a smooth projective algebraic curve over an algebraically closed field of characteristic zero.
6.
圆环内亚纯函数分担IM集合的唯一性定理 总被引:1,自引:0,他引:1
研究圆环内亚纯函数唯一性问题,获得了两个关于亚纯函数分担集合的一般性的唯一定理,从中得到了Nevanlinna五值定理的一个类似结果. 相似文献
7.
吴昭君 《数学物理学报(A辑)》2010,30(3):793-799
该文研究了复平面上的亚纯函数在角域内分担两个集合的唯一性,将仪洪勋和林伟川最近得到的复平面上的亚纯函数在全平面上分担两个集合的唯一性定理中的在全平面上分担两个集合的条件改成在角域内分担两个集合,得到了几个唯一性定理. 相似文献
8.
V. A. Skvortsov 《Mathematical Notes》1973,14(6):1011-1016
Criteria are found for the membership of multidimensional sets in the class of M-sets for multiple Haar series with various conditions imposed on the coefficients. Several generalizations of the uniqueness theorem are established.Translated from Matematicheskie Zametki, Vol. 14, No. 6, pp. 789–798, December, 1973. 相似文献
9.
关于亚纯函数的唯一性问题 总被引:7,自引:0,他引:7
本文应用 Nevanlinna理论研究亚纯函数的重值与唯一性问题,所得结果推广了某些已知的定理,并回答了C.C.Yang的一个猜测. 相似文献
10.
We study the problem of uniqueness of an element of the best L
1-approximation for continuous functions with values in a Banach space. We prove two theorems that characterize the uniqueness
subspaces in terms of certain sets of test functions. 相似文献
11.
Isaac Pesenson 《Transactions of the American Mathematical Society》2008,360(10):5603-5627
A notion of Paley-Wiener spaces on combinatorial graphs is introduced. It is shown that functions from some of these spaces are uniquely determined by their values on some sets of vertices which are called the uniqueness sets. Such uniqueness sets are described in terms of Poincare-Wirtinger-type inequalities. A reconstruction algorithm of Paley-Wiener functions from uniqueness sets which uses the idea of frames in Hilbert spaces is developed. Special consideration is given to the -dimensional lattice, homogeneous trees, and eigenvalue and eigenfunction problems on finite graphs.
12.
W. R. Wade 《Acta Mathematica Hungarica》2006,110(3):207-216
Summary We prove that under mild growth conditions, uniqueness holds for a multiple Walsh series whose square dyadic partial sums
converge almost everywhere to an integrable function. We apply this result to obtain a new uniqueness result for Cesáro summable
multiple Walsh series. 相似文献
13.
We prove a Tauberian theorem for Walsh series of two variables, and use it to obtain several results about uniqueness of Cesàro summable double Walsh series. Namely, we show that up to sets of measure zero, Cesàro summability of double Walsh series is the same as convergence of the square dyadic partial sums and, under a suitable growth condition, that uniqueness holds for Cesàro summable double Walsh series. 相似文献
14.
Ning Cui 《Journal of Difference Equations and Applications》2016,22(10):1452-1471
We mainly study the uniqueness of meromorphic functions sharing three distinct values CM with their difference operators, and the related result confirms the conjecture of Chen and Yi. We also obtain a uniqueness theorem on entire functions sharing two sets CM with their difference operators. 相似文献
15.
Victor L. Shapiro 《Proceedings of the American Mathematical Society》2003,131(11):3431-3440
This paper establishes non-Cartesian product sets, called fractal carpets and fractal foam, as sets of uniqueness for a class of trigonometric series.
16.
In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary. 相似文献
17.
Sets of relative uniqueness for Haar series are studied. Whole classes of conditions on the behavior of a Haar series, including the Arutyunyan--Talalyan condition, are considered. New numerical characteristic of perfect sets are introduced. They are used to obtain necessary conditions and sufficient conditions for a given set to be a set of relative uniqueness under certain assumptions. Thereby, the 1967 results of G. M. Mushegyan are generalized. Moreover, for 0<p<2, the existence of perfect U-sets with the G(p)-conditions introduced by W. Wade in 1981 is proved and a method for constructing such sets is given. 相似文献
18.
§ 1. Introduction Inthispaper,unlessspecified ,allthefunctionsarenonconstantmeromorphicfunctions.WeshallusethestandardnotatiosofNevanlinnatheoryofmeromorphicfunctionssuchasT(r,f) ,m(r ,f) ,N(r ,f) , N(r,f) ,… .SetE(r ,f) =∪α∈S{z|f(z) -a},whereaze ropointwithmultiplicitymiscountedmtimesintheset.AsetSsuchthatforanytwonon constantentirefunctionsf(z)andg(z)theconditionE(S ,f) =E(S ,g)impliesf≡ giscalledauniquerangesetsofentirefunctions.In 1 976,GROSSF [1 ]askedthefollowingquesti… 相似文献
19.
The purpose of this article is to investigate the uniqueness of meromorphic functions that share three or two finite sets on annuli. 相似文献
20.
S. P. Preobrazhenskii 《Journal of Mathematical Sciences》1984,27(1):2539-2545
One investigated closed uniqueness sets on U for the class of analytic functions in the unit circle U for which The fundamental result of the paper allows the construction of sufficiently small closed uniqueness sets for the above-specified class of functions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 180–190, 1983.This, according to the well-known boundary uniqueness theorem, proves that f(z)=0. 相似文献