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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.
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   

3.
We give the asymptotics of the sum , where , for the multiplicative functions , and .  相似文献   

4.
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   

5.
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   

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.
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   

8.
Let E be a normed space, and . Let . We give some exact formulas for 7#x03C4;.  相似文献   

9.
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   

10.
We point out an interplay between -Frobenius non-classical plane curves and complete -arcs in . A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete -arcs with parameters and being a power of the characteristic. In addition, for q a square, new complete -arcs with either and or and are constructed by using certain reducible plane curves.  相似文献   

11.
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   

12.
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   

13.
Determinants of Matrices Associated with Incidence Functions on Posets   总被引:3,自引:1,他引:2  
Let S = x 1,...,x n} be a finite subset of a partially ordered set P. Let f be an incidence function of P. Let denote the n × n matrix having f evaluated at the meet of x i and x j as its i, j-entry and denote the n × n matrix having f evaluated at the join of x i and x j as its i, j-entry. The set S is said to be meet-closed if for all 1 i, j n. In this paper we get explicit combinatorial formulas for the determinants of matrices and on any meet-closed set S. We also obtain necessary and sufficient conditions for the matrices and on any meet-closed set S to be nonsingular. Finally, we give some number-theoretic applications.  相似文献   

14.
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   

15.
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   

16.
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   

17.
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   

18.
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   

19.
Ouhabaz  El Maati 《Positivity》1999,3(1):83-93
Let be a contraction semigroup on the space of vector valued functions ( is a Hilbert space). In order to study the extension of to a contaction semigroup on , Shigekawa [Sh] studied recently the domination property where is a symmetric sub-Markovian semigroup on . He gives in the setting of square field operators sufficient conditions for the above inequality. The aim of the present paper is to show that the methods of [12] and [13] can be applied in the present setting and provide two ways for the extension of to We give necessary and sufficient conditions in terms of sesquilinear forms for the contractivity property as well as for the above domination property in a more general situation.  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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