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1.
Bakhvalov  A. N. 《Mathematical Notes》2002,72(3-4):454-465
In this paper, we consider the behavior of rectangular partial sums of the Fourier series of continuous functions of several variables with respect to the trigonometric system. The Fourier series is called -convergent if the limit of rectangular partial sums over all indices for which for all j and k exists. In the space of arbitrary even dimension 2m we construct an example of a continuous function with an estimate of the modulus of continuity such that its Fourier series is -divergent everywhere for any .  相似文献   

2.
We give the asymptotics of the sum , where , for the multiplicative functions , and .  相似文献   

3.
In the canonical smooth fiber bundles endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups and construct -invariant generalizations of differentiable connections. In both regular and special cases of the representations of the relevant groups , we found all the affine nonholonomic -, -, and -connections of the first order (see [1]–[3]) possessing the local Lie groups of transformations and also described the respective -invariant planar connections.  相似文献   

4.
Let be the set of all primes, the field of all algebraic numbers, and Z the set of square-free natural numbers. We consider partially ordered sets of interpretability types such as , and , where AD is a variety of -divisible Abelian groups with unique taking of the pth root p(x) for every p , is a variety of -modules over a normal field , contained in , and Gn is a variety of n-groupoids defined by a cyclic permutation (12 ...n). We prove that , and are distributive lattices, with and where ub and ubf are lattices (w.r.t. inclusion) of all subsets of the set and of finite subsets of , respectively.Deceased.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 198–210, March–April, 2005.  相似文献   

5.
Khabibullin  B. N. 《Mathematical Notes》2001,70(3-4):560-573
Let be a sequence of complex numbers such that as . For close to the imaginary axis, upper bounds of the indicator of a nonzero entire function of exponential type with minimal growth vanishing on is obtained. These bounds give sufficient conditions for the system of exponents to be incomplete in an unbounded domain in .  相似文献   

6.
Majorants and Extreme Points of Unit Balls in Bernstein Spaces   总被引:1,自引:1,他引:0  
The Bernstein space B p () (1 $$ " align="middle" border="0"> 0) is the set of functions from L p( ) having Fourier transforms (in the sense of generalized functions) with supports in the compact segment [- , ]. Every function f has an analytic continuation onto the complex plane, which is an entire function of exponential type . The spaces B p ()\, are conjugate Banach spaces. Therefore, the closed unit ball in B p () has a rich set of extreme (boundary) points: coincides with the weakly * closed convex hull of its extreme points. Since, for 1< p< , B p () is a uniformly convex space, only the balls and have nontrivially arranged sets of extreme points. In this paper, in terms of zeros of entire functions, we obtain necessary and sufficient conditions of extremeness for functions from .  相似文献   

7.
Let E be a normed space, and . Let . We give some exact formulas for 7#x03C4;.  相似文献   

8.
Let be a reductive Lie algebra over an algebraically closed field of characteristic zero and an arbitrary -grading. We consider the variety , which is called the commuting variety associated with the -grading. Earlier it was proved by the author that is irreducible, if the -grading is of maximal rank. Now we show that is irreducible for and (E6,F4). In the case of symmetric pairs of rank one, we show that the number of irreducible components of is equal to that of nonzero non--regular nilpotent G 0-orbits in . We also discuss a general problem of the irreducibility of commuting varieties.  相似文献   

9.
Let be the j-fold iterated function of . Let and > 0 be fixed, Q be a prime, and let N k(Q|x) denote the number of those nx for which Q . We give the asymptotics of N k(Q|x) in the range .  相似文献   

10.
It is well known that imprimitive P-polynomial association schemes with are either bipartite or antipodal, i.e., intersection numbers satisfy either for all for all . In this paper, we show that imprimitive -polynomial association schemes with are either dual bipartite or dual antipodal, i.e., dual intersection numbers satisfy either .  相似文献   

11.
Introduce the notation: , is the union of two segments [-1,1] and [-1 + ,1+ ], is a noninteger number, is the Hölder class with exponent on The following result announced by the authors in [J. Math. Sci. 117 (2003), No. 3] is proved. There exist numbers a 1 ( ) , b 1 ( ) 0 depending only on such that for any there exists a polynomial , such that . Bibliography: 11 titles.  相似文献   

12.
In the paper, a discrete distribution of the Matsumoto zetafunction is considered. It is proved that the probability measure , converges weakly as .  相似文献   

13.
Ikonnikova  T. K. 《Mathematical Notes》2001,69(3-4):347-363
Suppose that k and l are integers such that and , M k is a set of numbers without kth powers, and . In this paper, we obtain asymptotic estimates of the sums over   相似文献   

14.
Large Deviations for Sums of Independent Heavy-Tailed Random Variables   总被引:1,自引:0,他引:1  
We obtain precise large deviations for heavy-tailed random sums , of independent random variables. are nonnegative integer-valued random variables independent of r.v. (X i )i N with distribution functions F i. We assume that the average of right tails of distribution functions F i is equivalent to some distribution function with regularly varying tail. An example with the Pareto law as the limit function is given.  相似文献   

15.
Let Int be the lattice of all intervals of an MV-algebra . In the present paper we investigate the relations between direct product decompositions of and (i) the lattice Int , or (ii) 2-periodic isometries on , respectively.  相似文献   

16.
Suppose that , , and are three discrete probability distributions related by the equation (E): , where denotes the k-fold convolution of In this paper, we investigate the relation between the asymptotic behaviors of and . It turns out that, for wide classes of sequences and , relation (E) implies that , where is the mean of . The main object of this paper is to discuss the rate of convergence in this result. In our main results, we obtain O-estimates and exact asymptotic estimates for the difference .  相似文献   

17.
Let K be a compact space, let X be a closed subspace of C(K), and let be a positive measure on K. The triple is said to be regular if, for any positive function and for any , there exists a function such that on K and . The case where K is the unit sphere in and the subspace X is invariant with respect to the unitary group is investigated. Sufficient spectral conditions and a necessary condition for the regularity of a triple are obtained. Connections with compactness of certain Hankel operators and applications to interpolation problems are presented. Bibliography: 16 titles.  相似文献   

18.
Panov  A. N. 《Mathematical Notes》2003,74(3-4):401-410
In this paper, Ore extensions in the class of Hopf algebras are studied. The classification theorem enables one to describe the Hopf--Ore extensions for the group algebras, for the algebras and , and for the quantum ax + b group.  相似文献   

19.
Let be i.i.d. random variables and let, for each and . It is shown that a.s. whenever the sequence of self-normalized sums S n /V n is stochastically bounded, and that this limsup is a.s. positive if, in addition, X is in the Feller class. It is also shown that, for X in the Feller class, the sequence of self-normalized sums is stochastically bounded if and only if   相似文献   

20.
We prove the following theorem. Let m and n be any positive integers with mn, and let be a subset of the n-dimensional Euclidean space n . For each i=1, . . . , m, there is a class of subsets M i j of Tn . Assume that for each i=1, . . . , m, that M i j is nonempty and closed for all i, j, and that there exists a real number B(i, j) such that and its jth component xjB(i, j) imply . Then, there exists a partition of {1, . . . , n} such that for all i and We prove this theorem based upon a generalization of a well-known theorem of Birkhoff and von Neumann. Moreover, we apply this theorem to the fair allocation problem of indivisible objects with money and obtain an existence theorem.  相似文献   

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