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1.
We establish a connection between the root vectors of operators with discrete spectrum over a Banach space and the vectors
of exponential type for these operators. The result is illustrated using the example of operators with discrete spectrum generated
by boundary-value problems for equations of elliptic type.
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 36–38. 相似文献
2.
D. Han D. Larson Z. Pan W. Wogen 《Proceedings of the American Mathematical Society》2007,135(3):713-723
It is an open problem whether every one-dimensional extension of a triangular operator admits a separating vector. We prove that the answer is positive for many triangular Hilbert space operators, and in particular, for strictly triangular operators. This is revealing, because two-dimensional extensions of such operators can fail to have separating vectors.
3.
Enrique Bendito ngeles Carmona Andr s M. Encinas 《Applied Numerical Mathematics》2004,50(3-4):343-370
Our aim is to set the foundations of a discrete vectorial calculus on uniform n-dimensional grids, that can be easily reformulated on general irregular grids. As a key tool we first introduce the notion of tangent space to any grid node. Then we define the concepts of vector field, field of matrices and inner products on the space of grid functions and on the space of vector fields, mimicking the continuous setting. This allows us to obtain the discrete analogous of the basic first order differential operators, gradient and divergence, whose composition define the fundamental second order difference operator. As an application, we show that all difference schemes, with constant coefficients, for first and second order differential operators with constant coefficients can be seen as difference operators of the form
for suitable choices of q,
and
. In addition, we characterize special properties of the difference scheme, such as consistency, symmetry and positivity in terms of q,
and
. 相似文献
4.
Juan Marín Jr. Steven M. Seubert 《Journal of Mathematical Analysis and Applications》2006,320(2):599-610
The purpose of this paper is to study cyclic vectors and invariant subspaces of operators on the space of entire functions having as eigenvectors the monomials zn. 相似文献
5.
Let Un ⊂ Cn[a, b] be an extended Chebyshev space of dimension n + 1. Suppose that f0 ∈ Un is strictly positive and f1 ∈ Un has the property that f1/f0 is strictly increasing. We search for conditions ensuring the existence of points t0, …, tn ∈ [a, b] and positive coefficients α0, …, αn such that for all f ∈ C[a, b], the operator Bn:C[a, b] → Un defined by satisfies Bnf0 = f0 and Bnf1 = f1. Here it is assumed that pn,k, k = 0, …, n, is a Bernstein basis, defined by the property that each pn,k has a zero of order k at a and a zero of order n − k at b. 相似文献
6.
Eva A. Gallardo-Gutierrez Jonathan R. Partington 《Proceedings of the American Mathematical Society》2008,136(1):119-126
We provide a criterion for the existence of a residual set of common hypercyclic vectors for an uncountable family of hypercyclic operators which is based on a previous one given by Costakis and Sambarino. As an application, we get common hypercyclic vectors for a particular family of hypercyclic scalar multiples of the adjoint of a multiplier in the Hardy space, generalizing recent results by Abakumov and Gordon and also Bayart. The criterion is applied to other specific families of operators.
7.
8.
By the well-known result of Brown, Chevreau and Pearcy, every Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic.
We show that each power bounded operator on a Hilbert space with spectral radius equal to one has a nonzero vector which is not supercyclic. Equivalently, the operator has a nontrivial closed invariant homogeneous subset. Moreover, the operator has a nontrivial closed invariant positive cone.
9.
Ali Aral Hatice Gül İnce İlarslan Gülen Başcanbaz Tunca 《Mathematical Methods in the Applied Sciences》2016,39(18):5140-5148
The present paper is concerned with the approximation properties of discrete version of Picard operators. We first give exact equalities for the moments of the operators. In calculations of these moments, Eulerian numbers play a crucial role. We discuss convergence of these operators in weighted spaces and give Voronovskaya‐type asymptotic formula. The weighted approximation of the operators in quantitative mean in terms of different modulus of continuities is also considered. We emphasize that the rate of convergence of the operators is better than the one obtained in 1 . Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
10.
A discrete, positive, weighted algebraic polynomial operator which is based on Gaussian quadrature is constructed. The operator is shown to satisfy the Jackson estimate and an optimal version is obtained. 相似文献
11.
12.
We extend relative oscillation theory to the case of Sturm-Liouville operators Hu=r−1(−′(pu′)+qu) with different p's. We show that the weighted number of zeros of Wronskians of certain solutions equals the value of Krein's spectral shift function inside essential spectral gaps. 相似文献
13.
Ian N. Deters Steven M. Seubert 《Journal of Mathematical Analysis and Applications》2007,334(2):1209-1219
The purpose of this paper is to study cyclic vectors and invariant subspaces of operators on the space of functions analytic on an open disk in the complex plane having as eigenvectors the monomials zn. 相似文献
14.
Kit C. Chan 《Journal of Mathematical Analysis and Applications》2008,337(1):646-658
We examine common supercyclic vectors for a path of operators. In particular, we show that the path consisting of convex combinations of two arbitrary unilateral weighted backward shifts has a dense Gδ set of common supercyclic vectors. Moreover, we show there exists a path with a dense Gδ set of common supercyclic vectors between a unilateral weighted backward shift which satisfies the Supercyclicity Criterion, and an operator which does not. Lastly, we provide an example of a path of unilateral weighted backward shifts that fails to have a common supercyclic vector. 相似文献
15.
C. Zălinescu 《Mathematical Methods of Operations Research》1987,31(3):A79-A101
In this paper there are stated asymptotic solvability results which yield a Farkas' lemma for sublinear functions and operators. Applications to duality for homogeneous programming and to necessary optimality conditions for nonlinear programming are given. Some closedness conditions used in the paper are also discussed.
Zusammenfassung In dieser Arbeit werden asymptotische Lösbarkeitsresultate angegeben, die ein Farkas-Lemma für sublineare Funktionen und Operatoren liefern. Es werden Anwendungen auf die Dualitätstheorie homogener Programme und auf notwendige Optimalitätsbedingungen der nichtlinearen Programmierung angegeben. Einige Abgeschlossenheitsvoraussetzungen, die in der Arbeit benutzt werden, werden diskutiert.相似文献
16.
It is shown that in a scattering theory with averaging the invariance principle of M. S. Birman and T. Kato (in its strong form) is always valid. 相似文献
17.
18.
19.
For discrete operators generated by Calderon–Zygmund kernels we consider certain finite-dimensional approximations. We compare an initial discrete operator with its finite-dimensional analogue and obtain invertibility conditions and approximation rate. The error estimate for approximate finite-dimensional solution of corresponding equation is given also for a special right-hand side. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
Nick Dungey 《Semigroup Forum》2009,78(2):226-237
For suitable bounded operator semigroups (e
tA
)
t≥0 in a Banach space, we characterize the estimate ‖Ae
tA
‖≤c/F(t) for large t, where F is a function satisfying a sublinear growth condition. The characterizations are by holomorphy estimates on the semigroup,
and by estimates on powers of the resolvent. We give similar characterizations of the difference estimate ‖T
n
−T
n+1‖≤c/F(n) for a power-bounded linear operator T, when F(n) grows faster than n
1/2 for large n. 相似文献