共查询到20条相似文献,搜索用时 46 毫秒
1.
Mingjin Wang 《Journal of Mathematical Analysis and Applications》2008,341(2):1487-1494
In this paper, we use the Andrews-Askey integral and the q-Chu-Vandermonde formula to derive a more general integral formula. Applications of the new integral formula are also given, which include to derive the q-Pfaff-Saalschütz formula and the terminating Sears's transformation formula. 相似文献
2.
In this paper we study the maximal operators and the convolution operators Tδ associated with multipliers of the form
3.
In this paper, we first give several operator identities involving the bivariate Rogers-Szegö polynomials. By applying the technique of parameter augmentation to the multiple q-binomial theorems given by Milne [S.C. Milne, Balanced summation theorems for U(n) basic hypergeometric series, Adv. Math. 131 (1997) 93-187], we obtain several new multiple q-series identities involving the bivariate Rogers-Szegö polynomials. These include multiple extensions of Mehler's formula and Rogers's formula. Our U(n+1) generalizations are quite natural as they are also a direct and immediate consequence of their (often classical) known one-variable cases and Milne's fundamental theorem for An or U(n+1) basic hypergeometric series in Theorem 1.49 of [S.C. Milne, An elementary proof of the Macdonald identities for , Adv. Math. 57 (1985) 34-70], as rewritten in Lemma 7.3 on p. 163 of [S.C. Milne, Balanced summation theorems for U(n) basic hypergeometric series, Adv. Math. 131 (1997) 93-187] or Corollary 4.4 on pp. 768-769 of [S.C. Milne, M. Schlosser, A new An extension of Ramanujan's summation with applications to multilateral An series, Rocky Mountain J. Math. 32 (2002) 759-792]. 相似文献
4.
Ming-Yi Lee Chin-Cheng Lin Ying-Chieh Lin 《Journal of Mathematical Analysis and Applications》2008,348(2):787-796
Let K be a generalized Calderón-Zygmund kernel defined on Rn×(Rn?{0}). The singular integral operator with variable kernel given by
5.
Andrew Bakan 《Journal of Mathematical Analysis and Applications》2008,339(1):197-216
For the sets , 1?p<∞, of positive finite Borel measures μ on the real axis with the set of algebraic polynomials P dense in Lp(R,dμ), we establish a majorization principle of their “boundaries,” i.e. for every there exists such that dμ/dν?1. A corresponding principle holds for the sets , p>0, of non-negative upper semi-continuous on R functions (weights) w such that P is dense in the space : For every there exists such that w?ω. 相似文献
6.
K.V. Storozhuk 《Journal of Mathematical Analysis and Applications》2007,332(2):1365-1370
If (Tt)t?0 is a bounded C0-semigroup in a Banach space X and there exists a compact subset K⊆X such that
7.
Ákos Császár 《Journal of Mathematical Analysis and Applications》2004,297(2):490-494
The paper presents a formula for the γ-interior of a set under special conditions for , more general than those in the previous paper [Acta Math. Hungar. 80 (1998) 89-93]. There are also some applications. 相似文献
8.
Wolfgang Knirsch Georg Schneider 《Journal of Mathematical Analysis and Applications》2006,320(1):403-414
In this paper we investigate Hankel operators with anti-holomorphic symbols ∈L2(C,m|z|), where are general Fock spaces. We will show that is not continuous if the corresponding symbol is not a polynomial . For polynomial symbols we will give necessary and sufficient conditions for continuity and compactness in terms of N and m. For monomials we will give a complete characterization of the Schatten-von Neumann p-class membership for p>0. Namely in case 2k<m the Hankel operators are in the Schatten-von Neumann p-class iff p>2m/(m−2k); and in case 2k?m they are not in the Schatten-von Neumann p-class. 相似文献
9.
Yutian Lei 《Journal of Mathematical Analysis and Applications》2007,334(2):1341-1362
This paper is concerned with the asymptotic behavior of the regularized minimizer uε=(uε1,uε2,…,uεn+1) of an energy functional
10.
Mohamed Barraa 《Journal of Mathematical Analysis and Applications》2008,347(1):315-322
In this paper we investigate perturbations of the regular spectrum of an upper triangular operator matrix such as acting on a Hilbert space H⊕K. 相似文献
11.
Sachin Gautam Ashish Kumar Srivastava Amitabha Tripathi 《Discrete Applied Mathematics》2008,156(12):2423-2428
Given graphs , where k≥2, the notation
12.
Quoc-Phong Vu 《Journal of Mathematical Analysis and Applications》2007,334(1):487-501
We study properties of solutions of the evolution equation , where B is a closable operator on the space AP(R,H) of almost periodic functions with values in a Hilbert space H such that B commutes with translations. The operator B generates a family of closed operators on H such that (whenever eiλtx∈D(B)). For a closed subset Λ⊂R, we prove that the following properties (i) and (ii) are equivalent: (i) for every function f∈AP(R,H) such that σ(f)⊆Λ, there exists a unique mild solution u∈AP(R,H) of Eq. (∗) such that σ(u)⊆Λ; (ii) is invertible for all λ∈Λ and . 相似文献
13.
G. Sampson 《Journal of Mathematical Analysis and Applications》2007,334(1):196-205
For aj,bj?1, j=1,2,…,d, we prove that the operator maps into itself for , where , and k(x,y)=φ(x,y)eig(x,y), φ(x,y) satisfies (1.2) (e.g. φ(x,y)=|x−y|iτ,τ real) and the phase g(x,y)=xa⋅yb. We study operators with more general phases and for these operators we require that aj,bj>1, j=1,2,…,d, or al=bl?1 for some l∈{1,2,…,d}. 相似文献
14.
Given a graph G, we construct an auxiliary graph with vertices such that the set of all stable sets of is in one-to-one correspondence with the set of all colorings of G. Then, we show that the Max-Coloring problem in G reduces to the Maximum Weighted Stable set problem in . 相似文献
15.
Ke-Ang Fu 《Journal of Mathematical Analysis and Applications》2009,356(1):280-287
Let be a strictly stationary sequence of positively associated random variables with mean zero and finite variance. Set , Mn=maxk?n|Sk|, n?1. Suppose . In this paper, we study the exact convergence rates of a kind of weighted infinite series of , and as ε↘0, respectively. 相似文献
16.
By means of a modified version of Cauchy's method for obtaining bilateral series identities, two new transformation formulas for bilateral basic hypergeometric series are derived. These contain several important identities for basic hypergeometric series as special cases, including the nonterminating q-Saalschütz summation, Bailey's very well-poised summation and the nonterminating Watson transformation. 相似文献
17.
Gerard J. Chang Jer-Jeong Chen David Kuo Sheng-Chyang Liaw 《Discrete Applied Mathematics》2007,155(8):1007-1013
For positive integers j?k, an L(j,k)-labeling of a digraph D is a function f from V(D) into the set of nonnegative integers such that |f(x)-f(y)|?j if x is adjacent to y in D and |f(x)-f(y)|?k if x is of distance two to y in D. Elements of the image of f are called labels. The L(j,k)-labeling problem is to determine the -number of a digraph D, which is the minimum of the maximum label used in an L(j,k)-labeling of D. This paper studies -numbers of digraphs. In particular, we determine -numbers of digraphs whose longest dipath is of length at most 2, and -numbers of ditrees having dipaths of length 4. We also give bounds for -numbers of bipartite digraphs whose longest dipath is of length 3. Finally, we present a linear-time algorithm for determining -numbers of ditrees whose longest dipath is of length 3. 相似文献
18.
Let be the signed edge domination number of G. In 2006, Xu conjectured that: for any 2-connected graph G of order n(n≥2), . In this article we show that this conjecture is not true. More precisely, we show that for any positive integer m, there exists an m-connected graph G such that . Also for every two natural numbers m and n, we determine , where Km,n is the complete bipartite graph with part sizes m and n. 相似文献
19.
X.R. Ma 《Journal of Mathematical Analysis and Applications》2009,353(1):320-328
By virtue of Shukla's well-known bilateral summation formula and Watson's transfor-mation formula, we extend the four-variable generalization of Ramanujan's reciprocity theorem due to Andrews to a six-variable one. Some novel variants of Ramanujan's reciprocity theorem and q-series identities are presented. 相似文献
20.
Jian-Hua Yin 《Discrete Mathematics》2009,309(8):2579-6276
An r-graph is a loopless undirected graph in which no two vertices are joined by more than r edges. An r-complete graph on m+1 vertices, denoted by , is an r-graph on m+1 vertices in which each pair of vertices is joined by exactly r edges. A non-increasing sequence π=(d1,d2,…,dn) of nonnegative integers is r-graphic if it is realizable by an r-graph on n vertices. Let be the smallest even integer such that each n-term r-graphic sequence with term sum of at least is realizable by an r-graph containing as a subgraph. In this paper, we determine the value of for sufficiently large n, which generalizes a conjecture due to Erd?s, Jacobson and Lehel. 相似文献