共查询到20条相似文献,搜索用时 31 毫秒
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Michael Solomyak 《Journal of Approximation Theory》2003,121(2):199-219
Some results on the approximation of functions from the Sobolev spaces on metric graphs by step functions are obtained. In particular, we show that the approximation numbers an of the embedding operator of the Sobolev space on a graph G of finite length |G| into the space , where μ is an arbitrary finite Borel measure on G, satisfy the inequality
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In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))n?0 and (U(n))n?0, which are ultimately periodic modulo m, e.g.
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Abdelhamid Boussejra 《Journal of Functional Analysis》2003,202(1):25-43
Let positive definite} be the matrix ball of rank n and let HD be the associated Hua operator. For a complex number λ, such that Reiλ>n−1 we give a necessary and sufficient condition on solutions F of the following Hua system of differential equations on D:
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Bc(G) denotes the cyclic bandwidth of graph G. In this paper, we obtain the maximum cyclic bandwidth of graphs of order p with adding an edge as follows:
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Bebe Prunaru 《Journal of Functional Analysis》2008,254(6):1626-1641
Let H be a complex Hilbert space and let {Tn}n?1 be a sequence of commuting bounded operators on H such that . Let denote the space of all operators X in B(H) for which and suppose that . We will show that there exists a triple {K,Γ,{Un}n?1} where K is a Hilbert space, Γ:K→H is a bounded operator and {Un}n?1⊂B(K) is a sequence of commuting normal operators with such that TnΓ=ΓUn for n?1, and for which the mapping Y?ΓYΓ∗ is a complete isometry from the commutant of {Un}n?1 onto the space . Moreover we show that the inverse of this mapping can be extended to a ∗-homomorphism
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Let be a sequence of i.i.d. random variables taking values in a real separable Hilbert space (H,‖⋅‖) with covariance operator Σ, and set Sn=X1+?+Xn, n?1. Let . We prove that, for any 1<r<3/2 and a>−d/2,
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Let H be a 4-uniform hypergraph on an n-element vertex set V containing no 4-book of 3 pages, i.e., a hypergraph of 4 quadruples with vertices {1,2,…,7} and edges {1234,1235,1236,4567}. Then for n>n0
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Gelu Popescu 《Journal of Functional Analysis》2008,254(4):1003-1057
In this paper, we initiate the study of a class of noncommutative domains of n-tuples of bounded linear operators on a Hilbert space H, where m?2, n?2, and p is a positive regular polynomial in n noncommutative indeterminates. These domains are defined by certain positivity conditions on p, i.e.,
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Yasuo Teranishi 《Discrete Mathematics》2002,257(1):183-189
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Xiaoling Zhang 《Linear algebra and its applications》2008,428(7):1610-1619
In this paper, we study the largest Laplacian spectral radius of the bipartite graphs with n vertices and k cut edges and the bicyclic bipartite graphs, respectively. Identifying the center of a star K1,k and one vertex of degree n of Km,n, we denote by the resulting graph. We show that the graph (1?k?n-4) is the unique graph with the largest Laplacian spectral radius among the bipartite graphs with n vertices and k cut edges, and (n?7) is the unique graph with the largest Laplacian spectral radius among all the bicyclic bipartite graphs. 相似文献
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For finite subsets A1,…,An of a field, their sumset is given by . In this paper, we study various restricted sumsets of A1,…,An with restrictions of the following forms:
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We find lower bounds on the difference between the spectral radius λ1 and the average degree of an irregular graph G of order n and size e. In particular, we show that, if n ? 4, then
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Let H be a Hilbert space and C be a nonempty closed convex subset of H, {Ti}i∈N be a family of nonexpansive mappings from C into H, Gi:C×C→R be a finite family of equilibrium functions (i∈{1,2,…,K}), A be a strongly positive bounded linear operator with a coefficient and -Lipschitzian, relaxed (μ,ν)-cocoercive map of C into H. Moreover, let , {αn} satisfy appropriate conditions and ; we introduce an explicit scheme which defines a suitable sequence as follows:
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Let U2(H) be the Banach-Lie group of unitary operators in the Hilbert space H which are Hilbert-Schmidt perturbations of the identity 1. In this paper we study the geometry of the unitary orbit
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Hahng-Yun Chu Dong Seung Kang 《Journal of Mathematical Analysis and Applications》2007,325(1):595-607
Let n?2 be an integer number. In this paper, we investigate the generalized Hyers-Ulam-Rassias stability in Banach spaces and also Banach modules over a Banach algebra and a C∗-algebra, and the stability using the alternative fixed point of an n-dimensional cubic functional equation in Banach spaces: