相关论文: Preasymptotics and asymptotics of approximation nu…
In this paper, we investigate optimal linear approximations ($n$-approximation numbers ) of the embeddings from the Sobolev spaces $H^r\ (r>0)$ for various equivalent norms and the Gevrey type spaces $G^{\alpha,\beta}\ (\alpha,\beta>0)$ on…
In this paper, we reveal a new connection between approximation numbers of periodic Sobolev type spaces, where the smoothness weights on the Fourier coefficients are induced by a (quasi-)norm $\|\cdot\|$ on $\mathbb{R}^d$, and entropy…
We continue the research on the asymptotic and preasymptotic decay of singular numbers for tensor product Hilbert-Sobolev type embeddings in high dimensions with special emphasis on the influence of the underlying dimension $d$. The main…
We investigate asymptotically sharp upper and lower bounds for the approximation numbers of the compact Sobolev embeddings $\overset{\circ}{W}{^m}(\Omega)\hookrightarrow L_2(\Omega)$ and $ W^m(\Omega)\hookrightarrow L_2(\Omega)$, defined on…
In this paper, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences ${\bf a}=\{a_j\}_{j\geq1}$ and ${\bf b}=\{b_j\}_{j\geq1}$ of positive numbers. We obtain strong equivalences…
We investigate the approximation of $d$-variate periodic functions in Sobolev spaces of dominating mixed (fractional) smoothness $s>0$ on the $d$-dimensional torus, where the approximation error is measured in the $L_2-$norm. In other…
In this paper, we investigate the approximation problem for functions in Gaussian Sobolev spaces $W^s_p(\mathbb{R}^d, \gamma)$ of smoothness $s > 0$, where the approximation error is measured in the Gaussian Lebesgue space…
We prove asymptotic formulas for the behavior of approximation, Gelfand, Kolmogorov and Weyl numbers of Sobolev embeddings between Besov and Triebel-Lizorkin spaces defined on quasi-bounded domains.
In this paper, we study the approximation problem for functions in the Gaussian-weighted Sobolev space $W^\alpha_p(\mathbb{R}^d, \gamma)$ of mixed smoothness $\alpha \in \mathbb{N}$ with error measured in the Gaussian-weighted space…
We study the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of the compact embeddings of weighted function spaces of Besov and Triebel-Lizorkin type in the case where the weights belong to a large class. We obtain…
We prove embedding theorems for fully anisotropic Besov spaces. More concrete, inequalities between modulus of continuity in different metrics and of Sobolev type are obtained. Our goal is to get sharp estimates for some anisotropic cases…
The paper is dedicated to the study of embeddings of the anisotropic Besov spaces $B^{\beta_1,...,beta_n}_{p;\theta_1,...,\theta_n}(\Bbb R^n)$ into Lorentz spaces. We find the sharp asymptotic behaviour of embedding constants when some of…
The approximation numbers of the $L_2$-embedding of mixed order Sobolev functions on the $d$-torus are well studied. They are given as the nonincreasing rearrangement of the $d$-th tensor power of the approximation number sequence in the…
We study the embeddings of (homogeneous and inhomogeneous) anisotropic Besov spaces associated to an expansive matrix $A$ into Sobolev spaces, with focus on the influence of $A$ on the embedding behaviour. For a large range of parameters,…
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 dominating mixed smoothness into Lebesgue spaces.
In this paper we study the Gelfand and Kolmogorov numbers of Sobolev embeddings between weighted function spaces of Besov and Triebel-Lizorkin type with polynomial weights. The sharp asymptotic estimates are determined in the so-called…
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}^d)$ and $\mathcal{A}^{s,r}_{\rm mix}(\mathbb{T}^d) \to…
Sharp upper and lower estimates are obtained of the approximation numbers of a Sobolev embedding and an integral operator of Volterra type. These lead to asymptotic formulae for the approximation numbers and certain other s-numbers.
We continue our study on the logarithmic balanced model metric initiated in our previous work. By a non-trivial refinement of the set of tools developed in our previous work, we are able to confirm partially a conjecture we made in our…
We consider the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of compact embeddings between 2-microlocal Besov spaces with weights defined in terms of the distance to a $d$-set $U\subset \mathbb{R}^n$. The sharp…