共查询到10条相似文献,搜索用时 109 毫秒
1.
S. V. Shvedenko 《Mathematical Notes》1974,15(1):56-61
In this article we study, for a Hilbert spaceB of analytic functions in the open unit disk, the dependence of the structure of the space of sequencesB(Z)={{f(zk)} k=1 ∞ :f∈B} on the choice of the sequence Z={zk} k=1 ∞ of distinct points of the unit disk [6]. 相似文献
2.
We study the asymptotic behavior of the eigenvalues the Sturm-Liouville operator Ly = ?y″ + q(x)y with potentials from the Sobolev space W 2 θ?1 , θ ≥ 0, including the nonclassical case θ ∈ [0, 1) in which the potential is a distribution. The results are obtained in new terms. Let s 2k (q) = λ k 1/2 (q) ? k, s 2k?1(q) = μ k 1/2 (q) ? k ? 1/2, where {λ k } 1 ∞ and {μ k } 1 ∞ are the sequences of eigenvalues of the operator L generated by the Dirichlet and Dirichlet-Neumann boundary conditions, respectively,. We construct special Hilbert spaces t 2 θ such that the mapping F:W 2 θ?1 →t 2 θ defined by the equality F(q) = {s n } 1 ∞ is well defined for all θ ≥ 0. The main result is as follows: for θ > 0, the mapping F is weakly nonlinear, i.e., can be expressed as F(q) = Uq + Φ(q), where U is the isomorphism of the spaces W 2 θ?1 and t 2 θ , and Φ(q) is a compact mapping. Moreover, we prove the estimate ∥Ф(q)∥τ ≤ C∥q∥θ?1, where the exact value of τ = τ(θ) > θ ? 1 is given and the constant C depends only on the radius of the ball ∥q∥θ? ≤ R, but is independent of the function q varying in this ball. 相似文献
3.
Let K = F(T) be the rational function field over a finite field of q elements. For any polynomial f(T) ∈ F [T] with positive degree, denote by Λ f the torsion points of the Carlitz module for the polynomial ring F[T]. In this short paper, we will determine an explicit formula for the analytic class number for the unique subfield M of the cyclotomic function field K(Λ P ) of degree k over F(T), where P ∈ F[T] is an irreducible polynomial of positive degree and k > 1 is a positive divisor of q ? 1. A formula for the analytic class number for the maximal real subfield M + of M is also presented. Futhermore, a relative class number formula for ideal class group of M will be given in terms of Artin L-function in this paper. 相似文献
4.
В. Б. ШЕРСТЮКОВ 《Analysis Mathematica》2007,33(1):63-81
The paper is devoted to study the entire functions L(λ) with simple real zeros λk, k = 1, 2, ..., that admit an expansion of Krein’s type: $$\frac{1}{{\mathcal{L}(\lambda )}} = \sum\limits_{k = 1}^\infty {\frac{{c_k }}{{\lambda - \lambda _k }}} ,\sum\limits_{k = 1}^\infty {\left| {c_k } \right| < \infty } .$$ We present a criterion for these expansions in terms of the sequence {L′ (λ k )} k=1 ∞ . We show that this criterion is applicable to certain classes of meromorphic functions and make more precise a theorem of Sedletski? on the annihilating property in L 2 systems of exponents. 相似文献
5.
The aim of this paper is to prove the following extension of the Folkman-Rado-Sanders Finite Union Theorem: For every positive integersr andk there exists a familyL of sets having the following properties:
- ifS 1,S 2, ...,S k + 1 are distinct pariwise disjoint elements ofL then there exists nonemptyI ? {1, 2, ...,k + 1} with ∪ i∈I S i ?L
- ifL =L 1 ?...?L r is an arbitrary partition then there existsj ≤ r and pairwise disjoint setsS 1,S 2, ...,S k ∈L j , such thatL i∈I S i ∈L j for every nonemptyI ? {1, 2, ...,k}.
6.
Ben-Zion Rubshtein 《Journal of Theoretical Probability》1995,8(3):523-538
LetG be a compact group andM 1(G) be the convolution semigroup of all Borel probability measures onG with the weak topology. We consider a stationary sequence {μ n } n=?∞ +∞ of random measures μ n =μ n (ω) inM 1(G) and the convolutions $$v_{m,n} (\omega ) = \mu _m (\omega )* \cdots *\mu _{n - 1} (\omega ), m< n$$ and $$\alpha _n^{( + k)} (\omega ) = \frac{1}{k}\sum\limits_{i = 1}^k {v_{n,n + i} (\omega ),} \alpha _n^{( - k)} (\omega ) = \frac{1}{k}\sum\limits_{i = 1}^k {v_{n - i,n} (\omega )} $$ We describe the setsA m + (ω) andA n + (ω) of all limit points ofv m,n(ω) asm→?∞ orn→+∞ and the setA ∞(ω) of its two-sided limit points for typical realizations of {μ n (ω)} n=?∞ +∞ . Using an appropriate random ergodic theorem we study the limit random measures ρ n (±) (ω)=lim k→∞ α n (±k) (ω). 相似文献
7.
8.
LetX be ann-element set and letA and? be families of subsets ofX. We say thatA and? are crosst-intersecting if |A ∩ B| ≥ t holds for all A ∈A and for allB ∈ ?. Suppose thatA and ? are crosst-intersecting. This paper first proves a crosst-intersecting version of Harper's Theorem:
- There are two crosst-intersecting Hamming spheresA 0,? 0 with centerX such that |A| ≤ |A 0| and|?| ≤ |? 0| hold.
- Suppose thatt ≥ 2 and that the pair of integers (|A) is maximal with respect to direct product ordering among pairs of crosst-intersecting families. Then,A and? are Hamming spheres with centerX.
- Ifn + t = 2k ? 1 then |A| |?| ≤ max \(\left\{ {\left( {K_k^n + \left( {_{k - 1}^{n - 1} } \right)} \right)^2 ,K_k^n K_{k - 1}^n } \right\}\) holds, whereK l n is defined as \(\left( {_n^n } \right)\left( {_{n - 1}^n } \right) + \cdots + \left( {_l^n } \right).\)
- Ifn + t = 2k then |A| |? ≤ (K k n )2 holds.
9.
SupposeG n={G 1, ...,G k } is a collection of graphs, all havingn vertices ande edges. By aU-decomposition ofG n we mean a set of partitions of the edge setsE(G t ) of theG i , sayE(G t )== \(\sum\limits_{j = 1}^r {E_{ij} } \) E ij , such that for eachj, all theE ij , 1≦i≦k, are isomorphic as graphs. Define the functionU(G n) to be the least possible value ofr aU-decomposition ofG n can have. Finally, letU k (n) denote the largest possible valueU(G) can assume whereG ranges over all sets ofk graphs havingn vertices and the same (unspecified) number of edges. In an earlier paper, the authors showed that $$U_2 (n) = \frac{2}{3}n + o(n).$$ In this paper, the value ofU k (n) is investigated fork>2. It turns out rather unexpectedly that the leading term ofU k (n) does not depend onk. In particular we show $$U_k (n) = \frac{3}{4}n + o_k (n),k \geqq 3.$$ 相似文献
10.
Oleg Pikhurko 《Israel Journal of Mathematics》2014,201(1):415-454
The Turán density π(F) of a family F of k-graphs is the limit as n → ∞ of the maximum edge density of an F-free k-graph on n vertices. Let Π ∞ (k) consist of all possible Turán densities and let Π fin (k) ? Π ∞ (k) be the set of Turán densities of finite k-graph families. Here we prove that Π fin (k) contains every density obtained from an arbitrary finite construction by optimally blowing it up and using recursion inside the specified set of parts. As an application, we show that Π fin (k) contains an irrational number for each k ≥ 3. Also, we show that Π ∞ (k) has cardinality of the continuum. In particular, Π ∞ (k) ≠ Π fin (k) . 相似文献