Person: Cobos Díaz, Fernando
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First Name
Fernando
Last Name
Cobos Díaz
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Análisis Matemático Matemática Aplicada
Area
Análisis Matemático
Identifiers
18 results
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Now showing 1 - 10 of 18
Item Diversity of Lorentz-Zygmund spaces of operators defined by approximation numbers(Analysis Mathematica, 2023) Cobos Díaz, Fernando; Kühn, ThomasWe prove the following dichotomy for the spaces ℒ (a) p,q,α (X, Y) of all operators T ∈ ℒ(X, Y) whose approximation numbers belong to the Lorentz-Zygmund sequence spaces ℓp,q(log ℓ)α: If X and Y are infinite-dimensional Banach spaces, then the spaces ℒ (a) p,q,α (X, Y) with 0 < p < ∞, 0 < q ≤ ∞ and α ∈ ℝ are all different from each other, but otherwise, if X or Y are finite-dimensional, they are all equal (to ℒ(X, Y)). Moreover we show that the scale is strictly increasing in q, where ℒ (a) ∈,q (X, Y) is the space of all operators in ℒ(X, Y) whose approximation numbers are in the limiting Lorentz sequence space ∓∈,q.Item Approximation and entropy numbers of embeddings between approximation spaces(Constructive Approximation, 2018) Cobos Díaz, Fernando; Domínguez Bonilla, Óscar; Kühn, ThomasItem On a problem of Lions concerning real interpolation spaces. The quasi-Banach case(Journal of Mathematical Analysis and Applications, 2022) Cobos Díaz, Fernando; Cwikel, M.; Kühn, ThomasWe prove that, under a mild condition on a couple (A0;A1) of quasi-Banach spaces, all real interpolation spaces (A0;A1)θ,p with 0 < θ < 1 and 0 < p ≤ ∞ are different from each other. In the Banach case and for 1 ≤ p ≤ ∞ this was shown by Janson, Nilsson, Peetre and Zafran, thus solving an old problem posed by J.-L. Lions. Moreover, we give an application to certain spaces which are important objects in Operator Theory and which consist of bounded linear operators whose approximation numbers belong to Lorentz sequence spaces.Item Lorentz-Schatten classes and pointwise domination of matrices(Canadian Mathematical Bulletin, 1999) Cobos Díaz, Fernando; Kühn, ThomasWe investigate pointwise domination property in operator spaces generated by Lorentz sequence spacesItem On optimal approximation in periodic Besov spaces(Journal of Mathematical Analysis and Applications, 2019) Cobos Díaz, Fernando; Kühn, Thomas; Sickel, WinfriedWe work with spaces of periodic functions on the d-dimensional torus. We show that estimates for L∞-approximation of Sobolev functions remain valid when we replace L1 by the isotropic periodic Besov space B01;1 or the periodic Besovspace with dominating mixed smoothness S01;1B. For t > 1=2, we also prove estimates for L2-approximation of functions in the Besov space of dominating mixed smoothness St 1;1B, describing exactly the dependence of the involved constants on the dimension d and the smoothness t.Item On nuclearity of embeddings between Besov spaces(Journal of Approximation Theory, 2018) Cobos Díaz, Fernando; Domínguez Bonilla, Óscar; Kühn, ThomasLet Bp,qs,α(Ω) be the Besov space with classical smoothness s and additional logarithmic smoothness of order α on a bounded Lipschitz domain Ω in Rd. For s1, s2 ∈ R, 1 ≤ p1, p2, q1, q2 ≤ ∞ and s1 − s2 = d − d(1/p2 − 1/p1)+, we show a sufficient condition on q1, q2 for nuclearity of embedding Bs1,α1 (superíndices) y p1, q1 (subíndices)(Ω) → Bp2,α2 (superíndice) y s2 q,2 (subíndices) (Ω). We also show that the condition is necessary in a wide range of parameters.Item On the Optimal Asymptotic Eigenvalue Behavior of Weakly Singular Integral-Operators(Proceedings of the American Mathematical Society, 1991) Cobos Díaz, Fernando; Janson, Svante; Kühn, ThomasWe improve the known results on eigenvalue distributions of weakly singular integral operators having (power) order of the singularity equal to half of the dimension of the underlying domain. Moreover we show that our results are the best possible.Item Remarks on symmetries of trilinear forms(Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales., 2000) Cobos Díaz, Fernando; Kühn, Thomas; Peetre, JaakWe investigate the interplay between the different kinds of symmetry that a trihnear form may have and the behaviour of its norm.Item Eigenvalues of Weakly Singular Integral-Operators(Journal of the London Mathematical Society. Second Series, 1990) Cobos Díaz, Fernando; Kühn, ThomasWe determine the asymptotic order of decay of eigenvalues of weakly singular integral operators. The singularities are of quite general form, containing power and logarithmic terms. We give a unified elementary proof of all known results in this area. Our approach applies also in the case where the power order of the singularity is equal to the dimension of the domain and the logarithmic order is less than — 1. This case has not been considered previously. Furthermore, we show the optimality of the upper estimates in a rather strong sense. In particular, we give a partial positive answer to the conjecture of [3].Item Entropy and Eigenvalues of Weakly Singular Integral-Operators(Integral Equations and Operator Theory, 1988) Kühn, Thomas; Cobos Díaz, Fernando