33 citations · 48 across the 19 of their papers we have counts for
16 papers · 1 filter
Triebel - Lizorkin spaces of dominating mixed smoothness are algebras with respect to pointwise multiplication
Van Kien Nguyen
We continue our investigations on pointwise multipliers for spaces of dominating mixed smoothness. In this paper we prove that under a certain conditions Triebel - Lizorkin spaces…
Widths of embeddings of Gaussian Sobolev spaces
Van Kien Nguyen
In this paper, we investigate the approximation problem for functions in Gaussian Sobolev spaces of smoothness , where the approximation error is me…
Pseudo -Numbers of Embeddings of Gaussian Weighted Sobolev Spaces
Van Kien Nguyen
In this paper, we study the approximation problem for functions in the Gaussian-weighted Sobolev space of mixed smoothness with error mea…
Best -term approximation of diagonal operators and application to function spaces with mixed smoothness
Van Kien Nguyen, Van Dung Nguyen
In this paper we give exact values of the best -term approximation widths of diagonal operators between and with . Th…
-Numbers of Embeddings of Weighted Wiener Algebras
Van Dung Nguyen, Van Kien Nguyen, Winfried Sickel
In this paper we study the asymptotic behavior of Kolmogorov, approximation, Bernstein and Weyl numbers of embeddings $ \mathcal{A}^{s,r}_{\rm mix}(\mathbb{T}^d) \to L_2(\mathbb{T}…
Greedy Algorithms and Kolmogorov Widths in Banach Spaces
Van Kien Nguyen
Let be a Banach space and be a compact subset in . We consider a greedy algorithm for finding an -dimensional subspace which can be used to a…
Pointwise Multipliers for Besov Spaces of Dominating Mixed Smoothness - II
Van Kien Nguyen, Winfried Sickel
We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes $S^r_{p,q}B(\mathbb{…
On a Problem of Jaak Peetre Concerning Pointwise Multipliers of Besov Spaces
Van Kien Nguyen, Winfried Sickel
We characterize the set of all pointwise multipliers of the Besov spaces under the restrictions and .
Isotropic and Dominating Mixed Lizorkin - Triebel Spaces - a Comparison
Van Kien Nguyen, Winfried Sickel
We shall compare isotropic Lizorkin-Triebel spaces with their counterparts of dominating mixed smoothness.
Pointwise Multipliers for Sobolev and Besov Spaces of Dominating Mixed Smoothness
Van Kien Nguyen, Winfried Sickel
Under certain restrictions we describe the set of all pointwise multipliers in case of Sobolev and Besov spaces of dominating mixed smoothness. In addition we shall give necessary…
Gelfand Numbers of Embeddings of Mixed Besov Spaces
Van Kien Nguyen
Gelfand numbers represent a measure for the information complexity which is given by the number of information needed to approximate functions in a subset of a normed space with an…
Isotropic and Dominating Mixed Besov Spaces - a Comparison
Van Kien Nguyen, Winfried Sickel
We compare Besov spaces with isotropic smoothness with Besov spaces of dominating mixed smoothness. Necessary and sufficient conditions for continuous embeddings will be given.
Weyl and Bernstein Numbers of Embeddings of Sobolev Spaces with Dominating Mixed Smoothness
Van Kien Nguyen
This paper is a continuation of the papers [21] and [22]. Here we shall investigate the asymptotic behaviour of Weyl and Bernstein numbers of embeddings of Sobolev spaces with domi…
Kolmogorov Numbers of Embeddings of Besov Spaces of Dominating Mixed Smoothness into
Van Kien Nguyen
In this paper we shall give two-sided sharp estimates of Kolmogorov numbers of embeddings of the Besov spaces with dominating mixed smoothness into $ L_{\inft…
Bernstein Numbers of Embeddings of Isotropic and Dominating Mixed Besov Spaces
Van Kien Nguyen
The purpose of the present paper is to investigate the decay of Bernstein numbers of the embedding from into the space . The asymptotic be…
Weyl Numbers of Embeddings of Tensor Product Besov Spaces
Van Kien Nguyen, Winfried Sickel
In this paper we investigate the asymptotic behaviour of Weyl numbers of embeddings of tensor product Besov spaces into Lebesgue spaces. These results will be compared with the kno…