Search results for "Linear"
showing 10 items of 7165 documents
On symplectically rigid local systems of rank four and Calabi–Yau operators
2013
AbstractWe classify all Sp4(C)-rigid, quasi-unipotent local systems and show that all of them have geometric origin. Furthermore, we investigate which of those having a maximal unipotent element are induced by fourth order Calabi–Yau operators. Via this approach, we reconstruct all known Calabi–Yau operators inducing an Sp4(C)-rigid monodromy tuple and obtain closed formulae for special solutions of them.
On the structure of the similarity orbits of Jordan operators as analytic homogeneous manifolds
1989
For Jordan elementsJ in a topological algebraB with unite, an open groupB−1 of invertible elements and continuous inversion we consider the similarity orbitsS G (J)={gJg−1:g∈G} (G the groupB−1⋂{e+c:c∈I},I⊂B a bilateral continuous embedded topological ideal). We construct rational local cross sections to the conjugation mapping\(\pi ^J G \to S_G \left( J \right)\left( {\pi ^J \left( g \right) = gJg^{ - 1} } \right)\) and give to the orbitS G (J) the local structure of a rational manifold. Of particular interest is the caseB=L(H) (bounded linear operators on a separable Hilbert spaceH),I=B, for which we obtain the following: 1. If for a Hilbert space operator there exist norm continuous local…
Some coincidence and periodic points results in a metric space endowed with a graph and applications
2015
The purpose of this paper is to obtain some coincidence and periodic points results for generalized $F$-type contractions in a metric space endowed with a graph. Some examples are given to illustrate the new theory. Then, we apply our results to establishing the existence of solution for a certain type of nonlinear integral equation.
Multiplicity of solutions to a nonlinear boundary value problem of concave–convex type
2015
Abstract Problem (P) { − Δ p u + | u | p − 2 u = | u | r − 1 u x ∈ Ω | ∇ u | p − 2 ∂ u ∂ ν = λ | u | s − 1 u x ∈ ∂ Ω , where Ω ⊂ R N is a bounded smooth domain, ν is the unit outward normal at ∂ Ω , Δ p is the p -Laplacian operator and λ > 0 is a parameter, was studied in Sabina de Lis (2011) and Sabina de Lis and Segura de Leon (in press). Among other features, it was shown there that when exponents lie in the regime 1 s p r , a minimal positive solution exists if 0 λ ≤ Λ , for a certain finite Λ , while no positive solutions exist in the complementary range λ > Λ . Furthermore, in the radially symmetric case a second positive solution exists for λ varying in the same full range ( 0 , Λ ) …
Relations between natural and observable measures
2005
We give a complete description of relations between observable and natural measures in connection with invariance, ergodicity and absolute continuity.
Rolewicz-type chaotic operators
2015
In this article we introduce a new class of Rolewicz-type operators in l_p, $1 \le p < \infty$. We exhibit a collection F of cardinality continuum of operators of this type which are chaotic and remain so under almost all finite linear combinations, provided that the linear combination has sufficiently large norm. As a corollary to our main result we also obtain that there exists a countable collection of such operators whose all finite linear combinations are chaotic provided that they have sufficiently large norm.
Regularity and Algebras of Analytic Functions in Infinite Dimensions
1996
A Banach space E E is known to be Arens regular if every continuous linear mapping from E E to E ′ E’ is weakly compact. Let U U be an open subset of E E , and let H b ( U ) H_b(U) denote the algebra of analytic functions on U U which are bounded on bounded subsets of U U lying at a positive distance from the boundary of U . U. We endow H b ( U ) H_b(U) with the usual Fréchet topology. M b ( U ) M_b(U) denotes the set of continuous homomorphisms ϕ : H b ( U ) → C \phi :H_b(U) \to \mathbb {C} . We study the relation between the Arens regularity of the space E E and the structure of M b ( U ) M_b(U) .
Local multifractal analysis in metric spaces
2013
We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild regularity conditions. On the other hand, we consider a local spectrum that can be used to gain finer information on the local behaviour of measures than its global counterpart.
On the composition and decomposition of positive linear operators (VII)
2021
In the present paper we study the compositions of the piecewise linear interpolation operator S?n and the Beta-type operator B?n, namely An:= S?n ?B?n and Gn := B?n ? S?n. Voronovskaya type theorems for the operators An and Gn are proved, substantially improving some corresponding known results. The rate of convergence for the iterates of the operators Gn and An is considered. Some estimates of the differences between An, Gn, Bn and S?n, respectively, are given. Also, we study the behaviour of the operators An on the subspace of C[0,1] consisting of all polygonal functions with nodes {0, 1/2,..., n-1/n,1}. Finally, we propose to the readers a conjecture concerning the eigenvalues of the ope…
Grothendieck-type subsets of Banach lattices
2022
Abstract In the setting of Banach lattices the weak (resp. positive) Grothendieck spaces have been defined. We localize such notions by defining new classes of sets that we study and compare with some quite related different classes. This allows us to introduce and compare the corresponding linear operators.