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Kushpel, Alexander; Stábile, Régis Leandro Braguim; Tozoni, Sérgio Antonio

doi:10.1016/j.jat.2014.03.014

Cited by 12 publications

(5 citation statements)

References 15 publications

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“…Se Λ (2) = {λ k } k∈Z d , onde a função λ : [0, ∞) → Ré definida por λ(t) = e −γt r , γ, r > 0, temos que Λ (2) U p são conjuntos de funções infinitamente diferenciáveis (analíticas para r = 1).…”

Section: Resultsunclassified

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Estimativas para n-Larguras de Kolmogorov de conjuntos de funções finita e infinitamente diferenciáveis sobre o toro

Stábile¹,

Tozoni

2015

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. A teoria de n-larguras foi introduzida por Kolmogorov na década de 1930. Desde então, muitos trabalhos têm visado obter estimativas assintóticas para n-larguras de diferentes classes de conjuntos. Neste trabalho, investigamos n-larguras de Kolmogorov de operadores multiplicadores associados a conjuntos de funções finitamente e infinitamente diferenciáveis sobre o toro. Em particular, demonstramos que as estimativas obtidas são assonticamente exatas em termos de ordem em diversas situações.Palavras-chave. n-larguras, Kolmogorov, toro, operadores multiplicadores. IntroduçãoSeja A um subconjunto compacto e centralmente simétrico de um espaço de Banach X. Definimos a n-largura de Kolmogorov de A em X poronde oínfimoé tomado sobre todos os espaços n-dimensionais X n de X, tal valor nos diz o quão bem podemos aproximar o conjunto A por subespaços finito dimensionais de X. Se Yé um outro espaço de Banach e T : X −→ Y um operador limitado, definimos a n-Consideraremos operadores multiplicadores Λ = {λ k } k∈Z d , onde λ k = λ(|k|) para uma função real λ definida sobre [0, ∞) e | · | denota a norma euclidiana.1 registabile@ifsp.edu.br 2

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Section: Resultsunclassified

“…Teorema 2.2. Seja Λ (2) o operador multiplicador definido acima e R = γ dΓ(d/2)/2π d/2 r/d . Então para todo n ∈ N e 0 < r ≤ 1…”

Section: Resultsunclassified

Estimativas para n-Larguras de Kolmogorov de conjuntos de funções finita e infinitamente diferenciáveis sobre o toro

Stábile¹,

Tozoni

2015

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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“…It follows from [10] and [13] that for 1 ≤ p ≤ 2 ≤ q < ∞, the (2n) d -width of Kolmogorov of K * U p verifies…”

Section: Introductionmentioning

confidence: 90%

Optimal Approximation by $sk$-Splines on the Torus

Oliveira,

Tozoni

2018

Preprint

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Fixed a continuous kernel K on the d-dimensional torus, we consider a generalization of the univariate sk-spline to the torus, associated with the kernel K. It is proved an estimate which provides the rate of convergence of a given function by its interpolating sk-splines, in the norm of L q for functions of the type f = K * ϕ where ϕ ∈ L p and 1 ≤ p ≤ 2 ≤ q ≤ ∞, 1/p − 1/q ≥ 1/2. The rate of convergence is obtained for functions f in Sobolev classes and this rate gives optimal error estimate of the same order as best trigonometric approximation, in a special case.

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“…In [2,3,10,11,12,13,14,15,16,17,18] techniques were developed to obtain estimates for n-widths of multiplier operators defined for functions on torus and on two-points homogeneous spaces M d : S d , P d (R), P d (C), P d (H), P 16 (Cay). In this work we continue the development of methods of estimating n-widths of multiplier operators.…”

Section: Introductionmentioning

confidence: 99%

Estimates for $n$-widths of sets of smooth functions on complex spheres

Aleans¹,

Tozoni²

2019

Preprint

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In this work we investigate n-widths of multiplier operators Λ * and Λ, defined for functions on the complex sphere Ω d of C d , associated with sequences of multipliers of the type, respectively, for a bounded function λ defined on [0, ∞). If the operators Λ * and Λ are bounded from L p (Ω d ) into L q (Ω d ), 1 ≤ p, q ≤ ∞, and U p is the closed unit ball of L p (Ω d ), we study lower and upper estimates for the n-widths of Kolmogorov, linear, of Gelfand and of Bernstein, of the sets Λ * U p and ΛU p in L q (Ω d ). As application we obtain, in particular, estimates for the Kolmogorov n-width of classes of Sobolev, of finitely differentiable, infinitely differentiable and analytic functions on the complex sphere, in L q (Ω d ), which are order sharp in various important situations.

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Estimates forn-widths of sets of smooth functions on the torusTd

Cited by 12 publications

References 15 publications

Estimativas para n-Larguras de Kolmogorov de conjuntos de funções finita e infinitamente diferenciáveis sobre o toro

Estimativas para n-Larguras de Kolmogorov de conjuntos de funções finita e infinitamente diferenciáveis sobre o toro

Optimal Approximation by $sk$-Splines on the Torus

Estimates for $n$-widths of sets of smooth functions on complex spheres

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