On ill-posedness measures and space change in Sobolev scales

Zeitschrift für Analysis und ihre Anwendungen

Volumn 16, Issue 4, 1997, Pages 979-1000

  Hofmann, B ^a   Tautenhahn, U ^b  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

^b UNIVERSITY OF APPLIED SCIENCES ZITTAU GÖRLITZ   (Germany)

Author keywords

Compact linear operators; Degree of ill posedness; Embedding operators; Hilbert scale; Ill posed problems; Ill posedness measures; Interval of ill posedness; Sobolev scale; capacity

Indexed keywords

EID: 21944452909     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/800     Document Type: Article

References (16)

1. Baumeister, J.: Stable Solution of Inverse Problems. Braunschweig: Vieweg 1987.
2. Bertero, M. and P. Boccacci: An approach to inverse problems based on ε-entropy. In: Inverse Problems: Principles and Applications in Geophysics, Technology, and Medicine (eds.: G. Anger et al.). Berlin: Akademie-Verlag 1993, pp. 76 - 86.
3. Chang, S.-H.: A generalization of a theorem of Hille and Tamarkin with applications. Proc. London Math. Soc. (3) 2 (1952), 22 - 29.
4. Dicken, V. and P. Maaß: Wavelet-Galerkin methods for ill-posed problems. J. Inv. Ill-Posed Problems 4 (1996), 203 - 221.
5. Engl, H. W., Kunisch, K. and A. Neubauer: Convergence rates for Tikhonov regularization of non-linear ill-posed problems. Inv. Probl. 5 (1989), 523 - 540.
6. Engl, H. W., Hanke, M. and A. Neubauer: Regularization of Inverse Problems. Dordrecht: Kluwer 1996.
7. Gorenflo, R. and M. Yamamoto: Operator theoretic treatment of linear Abel integral equations of first kind. Preprint. Berlin: Free University, Dept. Math, and Comp. Sci., Preprint No. A-13/96.
8. Ha, C.-W.: Eigenvalues of differentiate positive definite kernels. SIAM J. Math. Anal. 17 (1986), 415 - 419.
9. Hofmann, B.: Regularization for Applied Inverse and Ill-Posed Problems (Teubner-Texte zur Mathematik: Vol. 85). Leipzig: B.G. Teubner Verlagsges. 1986.
10. Hofmann, B.: On the degree of ill-posedness for nonlinear problems. J. Inv. Ill-Posed Problems 2 (1994), 61 - 76.
11. Hofmann, B.: A local stability analysis of nonlinear inverse problems. Preprint. Chemnitz: Techn. Univ., Faculty of Math., Preprint IP2/1996. To appear in: Proc. Second Int. Conf. Inv. Probl. in Engin.: Theory and Practice. Le Croisic (France), June 1996.
12. Hofmann, B. and O. Scherzer: Factors influencing the ill-posedness of nonlinear problems. Inv. Probl. 10 (1994), 1277 - 1297.
13. Köhler, J. and U. Tautenhahn: Error bounds for regularized solutions of nonlinear ill-posed problems. J. Inv. Ill-Posed Problems 3 (1995), 47 - 74.
14. König, H.: Eigenvalue Distribution of Compact Operators. Basel: Birkhäuser 1986.
15. Krein, S. and Y. I. Petunin: Scales of Banach spaces. Russian Math. Surveys 21 (1966), 85 - 159.
16. Kolmogorov, A. N. and V. M. Tihomirov: ε-entropy and ε-capacity of sets in functional spaces. Amer. Math. Soc. Transl. (Ser. 2) 17 (1961), 277 - 364.