On the spectral radius in
E. Porada (1971)
Colloquium Mathematicae
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E. Porada (1971)
Colloquium Mathematicae
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K. Parthasarathy, R. Prakash (2006)
Studia Mathematica
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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
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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...
Krzysztof Zajkowski (2005)
Banach Center Publications
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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
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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...
Krzysztof Zajkowski (2010)
Studia Mathematica
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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...
Dario Fasino, Francesco Tudisco (2016)
Czechoslovak Mathematical Journal
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We propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix . The result exploits the Frobenius inner product between and a given rank-one landmark matrix . Different choices for may be used, depending on the problem under investigation. In particular, we show that the choice where is the all-ones matrix allows to estimate the signature of the leading eigenvector of , generalizing previous results on Perron-Frobenius properties of matrices...
Yoshishige Haraoka (2012)
Banach Center Publications
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For a Fuchsian system , (F) being distinct points in ℂ and , the number α of accessory parameters is determined by the spectral types , where . We call the set of α parameters a regular coordinate if all entries of the are rational functions in z. It is not yet known that, for any irreducibly realizable set of spectral types, a regular coordinate does exist. In this paper we study a process of obtaining a new regular coordinate from a given one by a coalescence of eigenvalues...
Boumediene Abdellaoui, Eduardo Colorado, Ireneo Peral (2004)
Journal of the European Mathematical Society
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In this work we study the problem in , in , on , in , is a bounded regular domain such that , , , , and are positive functions such that and . The main points under analysis are: (i) spectral instantaneous and complete blow-up related to the Harnack inequality in the case , ; (ii) the nonexistence of solutions if , ; (iii) a uniqueness result for weak solutions (in the distribution sense); (iv) further results on existence of weak solutions...
Andreas M. Fröhlich, Lutz Weis (2006)
Bulletin de la Société Mathématique de France
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We characterise the boundedness of the calculus of a sectorial operator in terms of dilation theorems. We show e. g. that if generates a bounded analytic semigroup on a UMD space, then the calculus of is bounded if and only if has a dilation to a bounded group on . This generalises a Hilbert space result of C.LeMerdy. If is an space we can choose another space in place of .
Alexandru Aleman, Anders Dahlner (2006)
Studia Mathematica
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We consider the quantization of inversion in commutative p-normed quasi-Banach algebras with unit. The standard questions considered for such an algebra A with unit e and Gelfand transform x ↦ x̂ are: (i) Is bounded, where ν ∈ (0,1)? (ii) For which δ ∈ (0,1) is bounded? Both questions are related to a “uniform spectral radius” of the algebra, , introduced by Björk. Question (i) has an affirmative answer if and only if , and this result is extended to more general nonlinear extremal...
Derrick Hart (2013)
Acta Arithmetica
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Let A be a multiplicative subgroup of . Define the k-fold sumset of A to be . We show that for . In addition, we extend a result of Shkredov to show that for .
Dubi Kelmer, Peter Sarnak (2009)
Journal of the European Mathematical Society
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The existence of a strong spectral gap for quotients of noncompact connected semisimple Lie groups is crucial in many applications. For congruence lattices there are uniform and very good bounds for the spectral gap coming from the known bounds towards the Ramanujan–Selberg conjectures. If has no compact factors then for general lattices a spectral gap can still be established, but there is no uniformity and no effective bounds are known. This note is concerned with the spectral...
D. Müller, E. Prestini (2010)
Colloquium Mathematicae
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We define partial spectral integrals on the Heisenberg group by means of localizations to isotropic or anisotropic dilates of suitable star-shaped subsets V containing the joint spectrum of the partial sub-Laplacians and the central derivative. Under the assumption that an L²-function f lies in the logarithmic Sobolev space given by , where is a suitable “generalized” sub-Laplacian associated to the dilation structure, we show that converges a.e. to f(x) as R → ∞.
Eva Löcherbach, Oleg Loukianov, Dasha Loukianova (2014)
Annales de l'I.H.P. Probabilités et statistiques
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Let be a -symmetric Hunt process on a LCCB space . For an open set , let be the exit time of from and be the generator of the process killed when it leaves . Let and . We give necessary and sufficient conditions for in terms of the behavior near the origin of the spectral measure of . When , , by means of this condition we derive the Nash inequality for the killed process. In the diffusion case this permits to show that the existence of moments of order for ...