共查询到20条相似文献,搜索用时 10 毫秒
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Consider an ergodic Markov operator \(M\) reversible with respect to a probability measure \(\mu \) on a general measurable space. It is shown that if \(M\) is bounded from \(\mathbb {L}^2(\mu )\) to \(\mathbb {L}^p(\mu )\), where \(p>2\), then it admits a spectral gap. This result answers positively a conjecture raised by Høegh-Krohn and Simon (J. Funct. Anal. 9:121–80, 1972) in the more restricted semi-group context. The proof is based on isoperimetric considerations and especially on Cheeger inequalities of higher order for weighted finite graphs recently obtained by Lee et al. (Proceedings of the 2012 ACM Symposium on Theory of Computing, 1131–1140, ACM, New York, 2012). It provides a quantitative link between hyperboundedness and an eigenvalue different from the spectral gap in general. In addition, the usual Cheeger inequality is extended to the higher eigenvalues in the compact Riemannian setting and the exponential behaviors of the small eigenvalues of Witten Laplacians at small temperature are recovered. 相似文献
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Stanislav Shkarin 《Journal of Mathematical Analysis and Applications》2011,382(2):516-522
We show that for every supercyclic strongly continuous operator semigroup {Tt}t?0 acting on a complex F-space, every Tt with t>0 is supercyclic. Moreover, the set of supercyclic vectors of each Tt with t>0 is exactly the set of supercyclic vectors of the entire semigroup. 相似文献
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Bernd Klöss 《Semigroup Forum》2010,81(3):461-482
In this paper we examine difference operators with constant coefficients. We show that the type of the generated semigroup is determined by a matrix mathbbBmathbb{B}, originating from the domain of the operator. Moreover, we provide necessary and sufficient conditions for exponential and polynomial stability of the semigroup in terms of the matrix mathbbBmathbb{B}, using results of A. Borichev and Y. Tomilov. We close the paper with an application of our results to flows in networks. 相似文献
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This paper concerns about the approximation by a class of positive exponential type multiplier operators on the unit sphere Sn of the (n + 1)- dimensional Euclidean space for n ≥2. We prove that such operators form a strongly continuous contraction semigroup of class (l0) and show the equivalence between the approximation errors of these operators and the K-functionals. We also give the saturation order and the saturation class of these operators. As examples, the rth Boolean of the generalized spherical Abel-Poisson operator +Vt^γ and the rth Boolean of the generalized spherical Weierstrass operator +Wt^k for integer r ≥ 1 and reals γ, k∈ (0, 1] have errors ||+r Vt^γ- f||X ω^rγ(f, t^1/γ)X and ||+rWt^kf - f||X ω^2rk(f, t^1/(2k))X for all f ∈ X and 0 ≤t ≤2π, where X is the Banach space of all continuous functions or all L^p integrable functions, 1 ≤p ≤+∞, on S^n with norm ||·||X, and ω^s(f,t)X is the modulus of smoothness of degree s 〉 0 for f ∈X. Moreover, +r^Vt^γ and +rWt^k have the same saturation class if γ= 2k. 相似文献
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Oleg V. Davydov 《manuscripta mathematica》1993,79(1):435-446
In this paper we affirmatively answer an open question raised by P. L. Butzer and W. Dickmeis in [2] and give a new general
theorem of the condensation of values for seminorm sequences. This continues our previous investigations [4]. 相似文献
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Let T = {T(t)}t ≥ 0 be a C0-semigroup on a Banach space X. In this paper, we study the relations between the abscissa ωLp(T) of weak p-integrability of T (1 ≤ p < ∞), the abscissa ωpR(A) of p-boundedness of the resolvent of the generator A of T (1 ≤ p ≤ ∞), and the growth bounds ωβ(T), β ≥ 0, of T. Our main results are as follows.
- 1. (i) Let T be a C0-semigroup on a B-convex Banach space such that the resolvent of its generator is uniformly bounded in the right half plane. Then ω1 − ε(T) < 0 for some ε > 0.
- 2. (ii) Let T be a C0-semigroup on Lp such that the resolvent of the generator is uniformly bounded in the right half plane. Then ωβ(T) < 0 for all β>¦1/p − 1/p′¦, 1/p + 1/p′ = 1.
- 3. (iii) Let 1 ≤ p ≤ 2 and let T be a weakly Lp-stable C0-semigroup on a Banach space X. Then for all β>1/p we have ωβ(T) ≤ 0.
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A semigroup of operators in convexity theory 总被引:1,自引:0,他引:1
Christer O. Kiselman 《Transactions of the American Mathematical Society》2002,354(5):2035-2053
We consider three operators which appear naturally in convexity theory and determine completely the structure of the semigroup generated by them.
RESUMO. Duongrupo de operatoroj en la teorio pri konvekseco. Ni konsideras tri operatorojn kiuj aperas nature en la teorio pri konvekseco kaj plene determinas la strukturon de la duongrupo generita de ili.
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Positivity - A special class of doubly stochastic (Markov) operators is constructed. In a sense these operators come from measure preserving transformations and inherit some of their properties,... 相似文献
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R. Drnovšek D. Kokol-Bukovšek L. Livshits G. MacDonald M. Omladič H. Radjavi 《Integral Equations and Operator Theory》2002,42(4):449-460
We construct an irreducible multiplicative semigroup of non-negative square-zero operators acting onL
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[0,1), for 1p<.The main idea for this paper was developed at the 2nd Linear Algebra Workshop at Bled, Slovenia, in June 1999.The work of the three Slovenian authors was supported by the Research Ministry of Slovenia.This author's work was supported by a Division grant from Colby College. 相似文献
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Vadim Kaimanovich 《Israel Journal of Mathematics》1995,89(1-3):77-134
Covering Markov operators are a measure theoretical generalization of both random walks on groups and the Brownian motion
on covering manifolds. In this general setup we obtain several results on ergodic properties of their Poisson boundaries,
in particular, that the Poisson boundary is always infinite if the deck group is non-amenable, and that the deck group action
on the Poisson boundary is amenable. For corecurrent operators we show that the Radon-Nikodym cocycles of two quotients of
the Poisson boundary are cohomologous iff these quotients coincide. It implies that the Poisson boundary is either purely
non-atomic or trivial, and that the action of any normal subgroup of the deck group on the Poisson boundary is conservative.
We show that the Poisson boundary is trivial for any corecurrent covering operator with a nilpotent (or, more generally, hypercentral)
deck group. Other applications and examples are discussed.
Supported by a British SERC Advanced Fellowship. A part of this work was done during my stay at MSRI, Berkeley supported by
NSF Grant DMS 8505550. 相似文献
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In this paper we consider iterates of Markov operators of the form where the j's are linearly independent, nonnegative and sum to 1. We define the evaluation matrix of Φ to be Φ* = [j(i/m)] and prove that the iterates of the operator converge in the operator norm if and only if the powers of the evaluation matrix converge. Utilizing results from the theory of Markov chains we obtain explicit expressions for the limiting operator when it exists. Finally, we apply these results to Bernstein operators and then to B-spline operators. 相似文献
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A. V. Pechkurov 《Mathematical Notes》2012,91(1-2):231-242
In the present paper, we describe the structure of a strongly continuous operator semigroup T(t) (where T: ?+ → End X and X is a complex Banach space) for which ImT(t) is a finite-dimensional space for all t > 0. It is proved that such a semigroup is always the direct sum of a zero semigroup and a semigroup acting in a finite-dimensional space. As examples of applications, we discuss differential equations containing linear relations, orbits of a special form, and the possibility of embedding an operator in a C 0-semigroup. 相似文献
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