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1.
Let Cn (, ) be the upper bound for deviations of periodic functions which form the Zygmund class Z,0 0<<2 from a class of positive linear operators. A study is made of the conditions under which there exists a limit nCn(, )=C(, ). An explicit expression is given for the functions C(,).Translated from Matematicheskie Zametki, Vol. 4, No. 2, pp. 201–210, August, 1968.  相似文献   

2.
Let A={a1,...,an} and B={b1,...,bm} be systems of distinct points in , let be a family of homotopic classes Hi,i=1,..., j+m, of closed Jordan curves on, where the classes Hj+l, l=1,...,m, consist of curves that are homotopic to a point curve in b. Let =1,..., j+m be a system of positive numbers and letU be the modulus of the extremal-metric problem for the family and the system . In this paper we investigate the dependence of the modulusU=U(,A,B) on the parameters i and on the disposition of the points ak and b. One shows thatU is a smooth function of the indicated arguments and one obtains expressions for the derivatives U, U, and U. One gives some applications of these results.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 72–82, 1985.  相似文献   

3.
Let K be respectively the parabolic biangle and the triangle in and be a sequence in [0, +[ such that limp (p)=+. According to Koornwinder and Schwartz,(7) for each there exist a convolution structure (*(p)) such that (K, *(p)) is a commutative hypergroup. Consider now a random walk on (K, *(p)), assume that this random walk is stopped after j(p) steps. Then under certain conditions given below we prove that the random variables on K admit a selective limit theorems. The proofs depend on limit relations between the characters of these hypergroups and Laguerre polynomials that we give in this work.  相似文献   

4.
Let Z t , t 0 be a strictly stable process on with index (0, 2]. We prove that for every p > , there exists = , p and such that
where || Z|| p stands for the strong p-variation of Z on [0,1]. The critical exponent p , takes a different shape according as | Z| is a subordinator and p > 1, or not. The small ball constant is explicitly computed when p > 1, and a lower bound on is easily obtained in the general case. In the symmetric case and when p > 2, we can also give an upper bound on in terms of the Brownian small ball constant under the (1/p)-Höder semi-norm. Along the way, we remark that the positive random variable is not necessarily stable when p > 1, which gives a negative answer to an old question of P. E. Greenwood.10  相似文献   

5.
Proper holomorphic mappings between generalized pseudoellipsoids   总被引:3,自引:0,他引:3  
Summary We characterize the existence of proper holomorphic mappings between pseudoellipsoids of the form . If f:()() is any such mapping, the existence of a subgroup of Aut (()) such that is shown equivalent to a condition on the branch locus of f.  相似文献   

6.
7.
Huaxin Lin 《K-Theory》1999,16(2):105-127
Let A be a unital nuclear separable C*-algebra which satisfies the Universal Coefficient Theorem and E be a unital essential extension of the form:
where is the C*-algebra of compact operators on l2. Suppose that Aut(E) is an automorphism on E. We show that if , the automorphism on A induced by , is in Aut0(A), the identity component of Aut(A), then is approximately inner if and only if an index ()=0. Consequently, in certain interesting cases, Aut0(E) if and only if [idE] in KK(E,E) and is approximately inner if and only if [idE] in KL(E,E). In particular, when K1(A) is torsion free, is approximately inner if and only if induces the identity map on K0(E).  相似文献   

8.
In this paper we show that the local time of the Brownian motion belongs to the Sobolev space for any p2 and 0<<1/p. In order to prove this result we first discuss the smoothness and integrability properties of the composition of the Dirac function with a Wiener integral W(h), and we show that this composition belongs to , for any >0 and p>1 such that +1/p>1.  相似文献   

9.
The following results are obtained: If >0, 2, [3, 4], andf is a nondecreasing (convex) function on [–1, 1] such thatE n (f) n for any n>, then E n (1) (f)Cn (E n (2) (f)Cn ) for n>, where C=C(), En(f) is the best uniform approximation of a continuous function by polynomials of degree (n–1), and E n (1) (f) (E n (2) (f)) are the best monotone and convex approximations, respectively. For =2 ( [3, 4]), this result is not true.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 9, pp. 1266–1270, September, 1994.  相似文献   

10.
Let k and d be any integers such that k 4 and . Then there exist two integers and in {0,1,2} such that . The purpose of this paper is to prove that (1) in the case k 5 and (,) = (0,1), there exists a ternary code meeting the Griesmer bound if and only if and (2) in the case k 4 and (,) = (0,2) or (1,1), there is no ternary code meeting the Griesmer bound for any integers k and d and (3) in the case k 5 and , there is no projective ternary code for any integers k and such that 1k-3, where and for any integer i 0. In the special case k=6, it follows from (1) that there is no ternary linear code with parameters [233,6,154] , [234,6,155] or [237,6,157] which are new results.  相似文献   

11.
Let log . We prove that there exist non-denumerably many pairwise not equivalent irrational numbers such that and where qn() denotes the denominator of the nth convergent of .  相似文献   

12.
For a finite setA of points in the plane, letq(A) denote the ratio of the maximum distance of any pair of points ofA to the minimum distance of any pair of points ofA. Fork>0 letc (k) denote the largest integerc such that any setA ofk points in general position in the plane, satisfying for fixed , contains at leastc convex independent points. We determine the exact asymptotic behavior ofc (k), proving that there are two positive constants=(), such thatk 1/3c (k)k 1/3. To establish the upper bound ofc (k) we construct a set, which also solves (affirmatively) the problem of Alonet al. [1] about the existence of a setA ofk points in general position without a 7-hole (i.e., vertices of a convex 7-gon containing no other points fromA), satisfying . The construction uses Horton sets, which generalize sets without 7-holes constructed by Horton and which have some interesting properties.  相似文献   

13.
Let the set of generalized polynomials having bounded coefficients beK={p= jgj. j j j,j=1, 2, ...,n}, whereg 1,g 2, ...,g n are linearly independent continuous functions defined on the interval [a, b], j, j are extended real numbers satisfying j<+, j>-, and j j. Assume thatf is a continuous function defined on a compact setX [a, b]. This paper gives the characterization theorem forp being the best uniform approximation tof fromK, and points out that the characterization theorem can be applied in calculating the approximate solution of best approximation tof fromK.  相似文献   

14.
An -universally extending ordered field of power is constructed for each regular power where 0 < On and . When is inaccessible, the structure is either a (set) model of J. H. Conway's ordered field No or an isomorphic copy of No depending on whether or not is a set or a proper class.Presented by Jan Mycielski.  相似文献   

15.
Summary Let (,,P) be a probability space and let {itX n ()} n=1 be a sequence of i.i.d. random vectors whose state space isZ m for some positive integerm, where Z denotes the integers. Forn = 1, 2,... letS n () be the random walk defined by . ForxZ m andU m, them-dimensional torus, let . Finally let be the characteristic function of the X's.In this paper we show that, under mild restrictions, there exists a set withP{ 0 } = 1 such that for 0 we have for all aU m,le0.As a consequence of this theorem, we obtain two corollaries. One is concerned with occupancy sets form-dimensional random walks, and the other is a mean ergodic theorem.Research supported by N.S.F. Grant # MCS 77-26809  相似文献   

16.
In this paper at first we introduce thesystem of total polar subspaces of an arbitrary k-diniensional plane with respect to the absolute (configuration) of an arbitrary n- dimensional CAYLEY/KLEIN space as a generalization of the total polar set of a regular k-plane of . Using the system of total polar sets of the intersection (n–2)-plane of two hyperplanes and we give the followingnew characterization of the angle of . and : for any straight line g with and g=Ø the angle of and is equal to the distance of the two intersection points of g with and .

Herrn Prof. Dr.Oswald Giering zum 60. Geburtstag gewidmet  相似文献   

17.
We have obtained an estimate, in terms of partial and mixed moduli, of the continuity of deviation of the Cesáro (C, ) means ( = (1,...,n),i , 1 > –1, ) of the sequence of rectangular partial sums ofn-multiple (n>1) conjugate trigonometric series from then-multiple truncated conjugate function. This estimate implies the result on them -convergence (1) of (C, ) means (1 > 0, ) provided that the essential conditions are imposed on the partial moduli of continuity. Finally, it is shown that them -convergence cannot be replaced by ordinary convergence.  相似文献   

18.
The series is studied, where Sn are the sums of independent equally distributed random variables, n is a sequence of nonnegative numbers, >0, and >0 is an arbitrary positive number. For a broad class of sequences n, the necessary and sufficient conditions are established for the convergence of this series for any >0.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 6, pp. 770–784, June, 1993.  相似文献   

19.
The semigroup of all transformations X of a finite (partially) ordered set , such that X for all , is considered. All possible generating sets of a are elucidated. Only one of those sets is irreducible. A system of defining relations is found for that generating set.Translated from Matematicheskie Zametki, Vol. 3, No. 6, pp. 657–662, June, 1968.  相似文献   

20.
Summary The local limit problem is investigated for sequences (p n ) of probability densities with stable limit densitiesq having characteristic exponent (0, 2).It is shown that certain continuity-properties (Hölder-continuity) are necessary and - under appropriate additional conditions-sufficient for asn. In this sence the speed of convergence is also studied.  相似文献   

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