On the spectral radius in
E. Porada (1971)
Colloquium Mathematicae
Similarity:
E. Porada (1971)
Colloquium Mathematicae
Similarity:
K. Parthasarathy, R. Prakash (2006)
Studia Mathematica
Similarity:
Relations between spectral synthesis in the Fourier algebra A(G) of a compact group G and the concept of operator synthesis due to Arveson have been studied in the literature. For an A(G)-submodule X of VN(G), X-synthesis in A(G) has been introduced by E. Kaniuth and A. Lau and studied recently by the present authors. To any such X we associate a -submodule X̂ of ℬ(L²(G)) (where is the weak-* Haagerup tensor product ), define the concept of X̂-operator synthesis and prove that a...
Herbert Koch, Fulvio Ricci (2007)
Studia Mathematica
Similarity:
Let n ≥ 1, d = 2n, and let (x,y) ∈ ℝⁿ × ℝⁿ be a generic point in ℝ²ⁿ. The twisted Laplacian has the spectrum n + 2k = λ²: k a nonnegative integer. Let be the spectral projection onto the (infinite-dimensional) eigenspace. We find the optimal exponent ϱ(p) in the estimate for all p ∈ [2,∞], improving previous partial results by Ratnakumar, Rawat and Thangavelu, and by Stempak and Zienkiewicz. The expression for ϱ(p) is ϱ(p) = 1/p -1/2 if 2 ≤ p ≤ 2(d+1)/(d-1), ϱ(p) = (d-2)/2 - d/p...
Huicai Jia, Jing Lou (2024)
Czechoslovak Mathematical Journal
Similarity:
For a set of graphs, an -factor of a graph is a spanning subgraph of , where each component of is contained in . It is very interesting to investigate the existence of factors in a graph with given minimum degree from the prospective of eigenvalues. We first propose a tight sufficient condition in terms of the -spectral radius for a graph involving minimum degree to contain a star factor. Moreover, we also present tight sufficient conditions based on the -spectral radius...
Krzysztof Zajkowski (2005)
Banach Center Publications
Similarity:
We consider operators acting in the space C(X) (X is a compact topological space) of the form , u ∈ C(X), where and are given continuous mappings (1 ≤ k ≤ N). A new formula on the logarithm of the spectral radius r(A) is obtained. The logarithm of r(A) is defined as a nonlinear functional λ depending on the vector of functions . We prove that , where Mes is the set of all probability vectors of measures on X × 1,..., N and λ* is some convex lower-semicontinuous functional on...
Dai Tamaki (2012)
Journal of the European Mathematical Society
Similarity:
For a real central arrangement , Salvetti introduced a construction of a finite complex Sal which is homotopy equivalent to the complement of the complexified arrangement in [Sal87]. For the braid arrangement , the Salvetti complex Sal serves as a good combinatorial model for the homotopy type of the configuration space of points in , which is homotopy equivalent to the space of k little -cubes. Motivated by the importance of little cubes in homotopy theory, especially in...
Ajoy Jana, M. Thamban Nair (2019)
Czechoslovak Mathematical Journal
Similarity:
It is known that the nonlinear nonhomogeneous backward Cauchy problem , with , where is a densely defined positive self-adjoint unbounded operator on a Hilbert space, is ill-posed in the sense that small perturbations in the final value can lead to large deviations in the solution. We show, under suitable conditions on and , that a solution of the above problem satisfies an integral equation involving the spectral representation of , which is also ill-posed. Spectral truncation...
Krzysztof Zajkowski (2010)
Studia Mathematica
Similarity:
We prove that for the spectral radius of a weighted composition operator , acting in the space , the following variational principle holds: , where X is a Hausdorff compact space, α: X → X is a continuous mapping preserving a Borel measure μ with suppμ = X, is the set of all α-invariant ergodic probability measures on X, and a: X → ℝ is a continuous and -measurable function, where . This considerably extends the range of validity of the above formula, which was previously known...
Haïkel Skhiri (2008)
Studia Mathematica
Similarity:
We show that the essential spectral radius of T ∈ B(H) can be calculated by the formula = inf: X an invertible operator, where is a Φ₁-perturbation function introduced by Mbekhta [J. Operator Theory 51 (2004)]. Also, we show that if is a Φ₂-perturbation function [loc. cit.] and if T is a Fredholm operator, then = sup: X an invertible operator.
Amir Mohammadi, Hee Oh (2015)
Journal of the European Mathematical Society
Similarity:
Let and for and when for , we obtain an effective archimedean counting result for a discrete orbit of in a homogeneous space where is the trivial group, a symmetric subgroup or a horospherical subgroup. More precisely, we show that for any effectively well-rounded family of compact subsets, there exists such that for an explicit measure on which depends on . We also apply the affine sieve and describe the distribution of almost primes on orbits of in arithmetic...
Teodor Banica (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
Associated to an Hadamard matrix is the spectral measure μ ∈ [0,N] of the corresponding Hopf image algebra, A = C(G) with . We study a certain family of discrete measures , coming from the idempotent state theory of G, which converge in Cesàro limit to μ. Our main result is a duality formula of type , where are the truncations of the spectral measures μ,ν associated to . We also prove, using these truncations , that for any deformed Fourier matrix we have μ = ν.
Vladimir Nikiforov (2016)
Czechoslovak Mathematical Journal
Similarity:
Let be a graph of order and the spectral radius of its adjacency matrix. We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in . One of the main results of the paper is the following theorem: Let and let be a graph of order , with minimum degree If then has a Hamiltonian cycle, unless or
Benedetto Silvestri
Similarity:
The work is dedicated to investigating a limiting procedure for extending “local” integral operator equalities to “global” ones in the sense explained below, and to applying it to obtaining generalizations of the Newton-Leibniz formula for operator-valued functions for a wide class of unbounded operators. The integral equalities considered have the form . (1) They involve functions of the kind , where X is a general locally compact space, F runs over a suitable class of Banach subspaces...
Felix Goldberg (2015)
Czechoslovak Mathematical Journal
Similarity:
The imbalance of an edge in a graph is defined as , where is the vertex degree. The irregularity of is then defined as the sum of imbalances over all edges of . This concept was introduced by Albertson who proved that (where ) and obtained stronger bounds for bipartite and triangle-free graphs. Since then a number of additional bounds were given by various authors. In this paper we prove a new upper bound, which improves a bound found by Zhou and Luo in 2008. Our bound involves...
Valentina Casarino, Paolo Ciatti (2009)
Studia Mathematica
Similarity:
By using the notion of contraction of Lie groups, we transfer estimates for joint spectral projectors from the unit complex sphere in to the reduced Heisenberg group hⁿ. In particular, we deduce some estimates recently obtained by H. Koch and F. Ricci on hⁿ. As a consequence, we prove, in the spirit of Sogge’s work, a discrete restriction theorem for the sub-Laplacian L on hⁿ.
Xiaodan Chen, Yaoping Hou (2015)
Czechoslovak Mathematical Journal
Similarity:
Let be the algebraic connectivity, and let be the Laplacian spectral radius of a -connected graph with vertices and edges. In this paper, we prove that with equality if and only if is the complete graph or . Moreover, if is non-regular, then where stands for the maximum degree of . Remark that in some cases, these two inequalities improve some previously known results.
Mbekezeli Nxumalo (2024)
Archivum Mathematicum
Similarity:
Given a topological space , let and denote, respectively, the Salbany compactification of and the compactification map called the Salbany map of . For every continuous function , there is a continuous function , called the Salbany lift of , satisfying . If a continuous function has a stably compact codomain , then there is a Salbany extension of , not necessarily unique, such that . In this paper, we give a condition on a space such that its Salbany map is open. In...