scholarly journals Sharp estimates for approximation numbers of non-periodic Sobolev embeddings

2019 ◽  
Vol 54 ◽  
pp. 101398 ◽  
Author(s):  
Therese Mieth
Keyword(s):  
Approximation Numbers ◽  
Sharp Estimates ◽  
Sobolev Embeddings

scholarly journals Trace operators on fractals, entropy and approximation numbers

2011 ◽  
Vol 18 (3) ◽  
pp. 549-575
Author(s):  
Cornelia Schneider
Keyword(s):  
Besov Spaces ◽  
Trace Operator ◽  
Approximation Numbers ◽  
Atomic Decompositions ◽  
Sharp Estimates ◽  
Compact Embeddings ◽  
Trace Space

Abstract First we compute the trace space of Besov spaces – characterized via atomic decompositions – on fractals Γ, for parameters 0 < p < ∞, 0 < q ≤ min(1, p) and s = (n – d)/p. New Besov spaces on fractals are defined via traces for 0 < p, q ≤ ∞, s ≥ (n – d)/p and some embedding assertions are established. We conclude by studying the compactness of the trace operator TrΓ by giving sharp estimates for entropy and approximation numbers of compact embeddings between Besov spaces. Our results on Besov spaces remain valid considering the classical spaces defined via differences. The trace results are used to study traces in Triebel–Lizorkin spaces as well.

scholarly journals Approximation numbers of Sobolev embeddings—Sharp constants and tractability

2014 ◽  
Vol 30 (2) ◽  
pp. 95-116 ◽  
Author(s):  
Thomas Kühn ◽  
Winfried Sickel ◽  
Tino Ullrich
Keyword(s):  
Sharp Constants ◽  
Approximation Numbers ◽  
Sobolev Embeddings

scholarly journals Counting Via Entropy: New Preasymptotics for the Approximation Numbers of Sobolev Embeddings

2016 ◽  
Vol 54 (6) ◽  
pp. 3625-3647 ◽  
Author(s):  
Thomas Kühn ◽  
Sebastian Mayer ◽  
Tino Ullrich
Keyword(s):  
Approximation Numbers ◽  
Sobolev Embeddings

scholarly journals Approximation numbers of Sobolev embeddings of radial functions on isotropic manifolds

2007 ◽  
Vol 5 (1) ◽  
pp. 27-48 ◽  
Author(s):  
Leszek Skrzypczak ◽  
Bernadeta Tomasz
Keyword(s):  
Asymptotic Formula ◽  
Sobolev Spaces ◽  
Symmetric Spaces ◽  
Approximation Numbers ◽  
Radial Functions ◽  
Sobolev Embeddings ◽  
Rank One

We regard the compact Sobolev embeddings between Besov and Sobolev spaces of radial functions on noncompact symmetric spaces of rank one. The asymptotic formula for the behaviour of approximation numbers of these embeddings is described.

Sign in / Sign up

Export Citation Format

Share Document