When Do Sobolev Spaces Form a Hilbert Scale?

DOI10.2307/2047179zbMath0665.46029OpenAlexW4249042212MaRDI QIDQ3816544

Andreas Neubauer

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2047179

zbMATH Keywords

Sobolev spacesHilbert scaleselfadjoint strictly positive operator in the Hilbert space

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Linear integral equations (45A05)

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Parameter identification from boundary measurements in a parabolic equation arising from geophysics ⋮ Some generalizations for Landweber iteration for nonlinear ill-posed problems in Hilbert scales ⋮ On the effect of noisy measurements of the regressor in functional linear models ⋮ On ill-posedness measures and space change in Sobolev scales ⋮ Adaptive estimation of linear functionals in functional linear models ⋮ Characterizations of adjoint Sobolev embedding operators with applications in inverse problems ⋮ A Projected Nesterov–Kaczmarz Approach to Stellar Population-Kinematic Distribution Reconstruction in Extragalactic Archaeology ⋮ Optimal weighting for linear inverse problems ⋮ Adaptive circular deconvolution by model selection under unknown error distribution ⋮ On rate optimal local estimation in functional linear regression ⋮ Bayesian linear inverse problems in regularity scales ⋮ Case Studies and a Pitfall for Nonlinear Variational Regularization Under Conditional Stability ⋮ Fast fully iterative Newton-type methods for inverse problems ⋮ On the stable estimation of flow geometry and wall shear stress from magnetic resonance images ⋮ Tikhonov regularization in Hilbert scales under conditional stability assumptions ⋮ Adaptive functional linear regression ⋮ Thresholding projection estimators in functional linear models

Cites Work

• Convergence Rates for Tikhonov Regularization in Finite-Dimensional Subspaces of Hilbert Scales
• An a Posteriori Parameter Choice for Tikhonov Regularization in Hilbert Scales Leading to Optimal Convergence Rates
• Regularization with Differential Operators. II: Weak Least Squares Finite Element Solutions to First Kind Integral Equations
• Error bounds for tikhonov regularization in hilbert scales
• SCALES OF BANACH SPACES
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