首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
In the present paper, two general theorems on summability factors of infinite series which generalize some known results, have been proved. Also we have obtained two new results concerning the |C,1;δ| k summability factors.  相似文献   

2.
In this paper using δ-quasi-monotone sequences a theorem on summability factors of infinite series, which generalizes a theorem of Bor [4] on summability factors of infinite series, is proved. Also, in the special case this theorem includes a result of Mazhar [8] on |C, 1|k summability factors.  相似文献   

3.
《Quaestiones Mathematicae》2013,36(6):803-809
Abstract

In this paper, we have extended a known theorem dealing with |, pn|k summability factors to the |A, pn|k summability under weaker conditions by using an almost increasing sequence  相似文献   

4.
For any positive real numbers A, B, and d satisfying the conditions , d>2, we construct a Gabor orthonormal basis for L2(ℝ), such that the generating function g∈L2(ℝ) satisfies the condition:∫|g(x)|2(1+|x| A )/log d (2+|x|)dx < ∞ and .  相似文献   

5.
Let II be a bounded symmetric domain, ω ⇉ I a bounded subdomain, and let denote the weighted Bergman space of holomorphic square integrable functions on I. Let Tλ, ω be the Berezin-Toeplitz operator on with symbol χΩ and kth eigenvalue λ k (T λ,Ω). We prove that for δ1 sufficiently close to 0 and δ2 sufficiently close to 1 the estimate
holds for all domains ω satisfying the condition |{z ∈ I |d(z, Ω) < ε}| ≤c|Ω|, where d is the invariant distance on I and |ω| is the invariant volume of ω. The proof is based on the fact that the operator norm of the Berezin transform is smaller than 1. Our main technical tool are some of the formulae for the Berezin transform obtained by Unterberger and Upmeier in [11].  相似文献   

6.
Let A 0, ... , A n−1 be operators on a separable complex Hilbert space , and let α0,..., α n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω n−1 are the n roots of unity with ω j = e ij/n , 0 ≤ jn − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso optained.   相似文献   

7.
Theorems determining Weyl's multipliers for the summability almost everywhere by the |c, 1| method of the series with respect to block-orthonormal systems are proved. In particular, it is stated that if the sequence {(n)} is the Weyl multiplier for the summability almost everywhere by the |c, 1| method of all orthogonal series, then there exists a sequence {N k} such that {(n)} will be the Weyl multiplier for the summability almost everywhere by the |c, 1| method of all series with respect to the k -orthonormal systems.  相似文献   

8.
In this paper a general theorem concerning the |A,δ|k summability methods has been proved, which generalizes two results of Şevli and Leindler [H. Şevli and L. Leindler, On the absolute summability factors of infinite series involving quasi-power-increasing sequences, Computers and Mathematics with Applications 57 (2009), 702–709]. We obtain sufficient conditions for ∑anλn to be summable |A,δ|k, k1, 0δ<1/k, by using quasi-power-increasing sequences.  相似文献   

9.
In this paper we consider special elements of the Fock space #x2131; n . That is the space of entire functionsf:ℂ: n →ℂ, such that the followingL 2- condition is satisfied: . Here we show that there exists an entire functiong:ℂ n →ℂ such that for every one-dimensional subspace Π⊂ℂ n and for all 0<∈<2 we have , but in the limit case ∈=0 we have . This result is analogue to a result from [1]. There holomorphic functions on the unit-ball are investigated. Furthermore the proof — as the one in [1] — uses a theorem from [2]. Therefore we give another application of the results from [2] — namely for spaces of entire functions.  相似文献   

10.
Some remarks on trigonometric sums   总被引:1,自引:1,他引:0  
Let
where m 1 < m 2 < … < m t ≦ , δ x → 0, p runs over the primes p ≧ ≦ 1, |X p | ≦ 1. It is assumed that m v , , X p may depend on x. Assume that . It is proved that
for almost all irrational α, π(x) = number of primes up to x. Research supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA T46993.  相似文献   

11.
We show that if f1, f2 are bounded holomorphic functions in the unit ball of ℂn such that , |f1(z)|2 + |f2(z)2|2 ≥ δ2 >; 0, then any functionh in the Hardy space ,p < +∞ can be decomposed ash = f1h1 + f2h2 with . The Corona theorem in would be the same result withp = +∞ and this question is still open forn ≳-2, but the preceding result goes in this direction.  相似文献   

12.
For entire functionsf whose power series have Hadamard gaps with ratio ≥1+α>1, Gaier has shown that the condition |f(x)|≤e x forx≥0 implies |f(z)|≤C αe|z| (*) for allz. Here the result is extended to the case of square root gaps, that is, , with , where α>0. Smaller gaps cannot work. In connection with his proof of the general high indices theorem for Borel summability, Gaier had shown that square root gaps imply . Having such an estimate, one can adapt Pitt’s Tauberian method for the restricted Borel high indices theorem to show that, in fact, , which implies (*). The author also states an equivalent distance formula involving monomialsx pke−xinL (0, ∞).  相似文献   

13.
In this paper, we prove the estimate
, for every δ ∈ (0, ℓN), where C = C(N) is a positive constant depending only on N and . We show that the constant ℓN in this estimate is optimal. We also present a class of maps from into , strictly larger than , on which we can define the notion of degree and for which the previous inequality still holds.  相似文献   

14.
Let (a, b) be a pair of non-negative numbers such that (1)a, b1 and (2)a+b3. Letu 1,...,u n be a sequence of vectors from the set {(x, y)R 2: |x|, |y|1}, withu 1+...+u n =0. It is shown that there is a permutation of indices such that all partial sumsu (1)+...+u (k) lie in the rectangle |x|a, |y|b. Conditions (1) and (2) are also necessary.  相似文献   

15.
It is shown in [4] that if a normal matrix,A satisfies some conditions then |C,1| k summability implies |A| k summability wherek≥1. In the present paper, we consider the converse implication.  相似文献   

16.
We study the boundary value problem in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝ N . Our attention is focused on two cases when , where m(x) = max{p 1(x), p 2(x)} for any x ∈ or m(x) < q(x) < N · m(x)/(Nm(x)) for any x ∈ . In the former case we show the existence of infinitely many weak solutions for any λ > 0. In the latter we prove that if λ is large enough then there exists a nontrivial weak solution. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with a ℤ2-symmetric version for even functionals of the Mountain Pass Theorem and some adequate variational methods.  相似文献   

17.
The paper is concerned with bounds for integrals of the type
, involving Jacobi polynomials p n (α,β) and Jacobi weights w (a,b) depending on α,β, a, b > −1, where the subsets U k (x) ⊂ [−1, 1] located around x and are given by with . The functions to be integrated will also be of the type on the domain [−1,1] t/ U k (x). This approach uses estimates of Jacobi polynomials modified Jacobi weights initiated by Totik and Lubinsky in [1]. Various bounds for integrals involving Jacobi weights will be derived. The results of the present paper form the basis of the proof of the uniform boundedness of (C, 1) means of Jacobi expansions in weighted sup norms in [3].   相似文献   

18.
In this paper, by using an almost increasing and δ-quasi-monotone sequence, a general theorem on φ- | C, α | k summability factors, which generalizes a result of Bor [3] on φ |C, 1| k summability factors, has been proved under weaker and more general conditions.  相似文献   

19.
Let G be a commutative semigroup and letL be a complete Archimedean Riesz Space. Suppose thatF: G → L satisfies for somee ∈ L + the inequality
Then there exists a unique additive mappingA : G → L such that
As the method of the proof we use the Johnson-Kist Representation Theorem.  相似文献   

20.
For arbitrary 0 ≤ σ ≤ ρ ≤ σ + 1, we describe the class A σ ρ of functions g(z) analytic in the unit disk = {z : ∣z∣ < 1} and such that g(z) ≠ 0, ρT[g] = σ, and ρM[g] = ρ, where
__________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 979–995, July, 2007.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号