Estimates of entropy numbers and Gaussian measures for classes of functions with bounded mixed derivative
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Publication:1266115
DOI10.1006/jath.1997.3157zbMath0904.41016OpenAlexW2023096683MaRDI QIDQ1266115
Publication date: 24 January 1999
Published in: Journal of Approximation Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jath.1997.3157
Trigonometric approximation (42A10) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)
Related Items (25)
Approximation of functions with small mixed smoothness in the uniform norm ⋮ Weyl and Bernstein numbers of embeddings of Sobolev spaces with dominating mixed smoothness ⋮ Estimates for entropy numbers of sets of smooth functions on the torus \(\mathbb{T}^d\) ⋮ Small deviations of stable processes and entropy of the associated random operators ⋮ Estimates for the entropy numbers of the Nikol'skii–Besov classes of functions with mixed smoothness in the space of quasi‐continuous functions ⋮ Characteristics of the linear and nonlinear approximations of the Nikol'skii-Besov-type classes of periodic functions of several variables ⋮ Estimation of the entropy numbers and Kolmogorov widths for the Nikol'skii-Besov classes of periodic functions of many variables ⋮ Best \(m\)-term approximation and Sobolev-Besov spaces of dominating mixed smoothness -- the case of compact embeddings ⋮ Metric entropy of integration operators and small ball probabilites for the Brownian sheet ⋮ Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol'skii-Besov spaces ⋮ Interpolation and integral norms of hyperbolic polynomials ⋮ An upper bound on the Kolmogorov widths of a certain family of integral operators ⋮ Weyl numbers of embeddings of tensor product Besov spaces ⋮ Monte Carlo methods for uniform approximation on periodic Sobolev spaces with mixed smoothness ⋮ On the entropy numbers of the mixed smoothness function classes ⋮ Nonlinear approximations using sets of finite cardinality or finite pseudo-dimension ⋮ Entropy numbers of the Nikol'skii-Besov-type classes of periodic functions of many variables ⋮ On a norm and approximate characteristics of classes of multivariable functions ⋮ Estimates of entropy numbers in probabilistic setting ⋮ Approximating characteristics of the classes of periodic multivariate functions in the space \(B_{ \infty , 1} \) ⋮ Approximation, metric entropy and small ball estimates for Gaussian measures ⋮ Estimates for the entropy numbers of the classes \( {B}_{p,\theta}^{\Omega } \) of periodic multivariable functions in the uniform metric ⋮ Kolmogorov widths of the Nikol'skii-Besov classes of periodic functions of many variables in the space of quasicontinuous functions ⋮ Small ball probabilities for the Slepian Gaussian fields ⋮ Approximation of the classes of periodic functions of one and many variables from the Nikol'skii-Besov and Sobolev spaces
Cites Work
- Probability estimates for multiparameter Brownian processes
- Gaussian measures in Banach spaces
- Metric entropy and the small ball problem for Gaussian measures
- The small ball problem for the Brownian sheet
- Interpolation theorems for classes of functions with dominating mixed derivative
- Approximation of zonoids by zonotopes
- An inequality for trigonometric polynomials and its application for estimating the entropy numbers
- On best \(m\)-term approximations and the entropy of sets in the space \(L^ 1\)
- Approximation of functions of several variables by trigonometric polynomials with given number of harmonics, and estimates of \(\epsilon\)- entropy
- Subspaces of Small Codimension of Finite-Dimensional Banach Spaces
- Metric entropy and approximation
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