Publications

Preprints

• J. Flemming, B. Hofmann: New aspects of ill-posedness classification in Banach spaces, arXiv:2511.06690 [math.FA], 2025
• J. Flemming: A simple linear time algorithm for smallest enclosing circles on the (hemi)sphere, arXiv:2407.19840 [cs.CG], 2024

Papers in refereed journals

• B. Hofmann, J. Flemming: A note on the Goldberg-Thorp example in light of the classification of linear ill-posed problems in Banach spaces, Journal of Inverse and III-posed Problems, 2026, accepted for publication; earlier version available at arXiv:2603.01183 [math.FA]
• S. Reichert, J. Flemming, Q. An, Y. Vaynzof, J.-F. Pietschmann, C. Deibel: Ionic-defect distribution revealed by improved evaluation of deep-level transient spectroscopy on perovskite solar cells, Physical Review Applied, 2020, volume 13, issue 3, page 034018, DOI: 10.1103/PhysRevApplied.13.034018; earlier version available at arXiv:1910.04583 [physics.app-ph]
• J. Flemming: A converse result for Banach space convergence rates in Tikhonov-type convex regularization of ill-posed linear equations, Journal of Inverse and III-posed Problems, 2018, volume 26, issue 5, pages 639-646, DOI: 10.1515/jiip-2017-0116; earlier version available at arXiv:1712.01499 [math.NA]
• J. Flemming: Existence of variational source conditions for nonlinear inverse problems in Banach spaces, Journal of Inverse and III-posed Problems, 2018, volume 26, issue 2, pages 277-286, DOI: 10.1515/jiip-2017-0092; earlier version available at arXiv:1709.05809 [math.NA]
• J. Flemming, D. Gerth: Injectivity and weak*-to-weak continuity suffice for convergence rates in l¹-regularization, Journal of Inverse and III-posed Problems, 2018, volume 26, issue 1, pages 85-94, DOI: 10.1515/jiip-2017-0008
• S. Bürger, J. Flemming, B. Hofmann: On complex-valued deautoconvolution of compactly supported functions with sparse Fourier representation, Inverse Problems, 2016, volume 32, issue 10, page 104006 (12pp), DOI: 10.1088/0266-5611/32/10/104006
• J. Flemming: Convergence rates for l¹-regularization without injectivity-type assumptions, Inverse Problems, 2016, volume 32, issue 9, page 095001 (19pp), DOI: 10.1088/0266-5611/32/9/095001
• J. Flemming, B. Hofmann, I. Veselic: A unified approach to convergence rates for l¹-regularization and lacking sparsity, Journal of Inverse and III-posed Problems, 2016, volume 24, issue 2, pages 139-148, DOI: 10.1515/jiip-2015-0058
• J. Flemming, B. Hofmann, I. Veselic: On l¹-regularization in Light of Nashed’s Ill-Posedness Concept, Computational Methods in Applied Mathematics, 2015, volume 15, issue 3, pages 279-289, DOI: 10.1515/cmam-2015-0008; earlier version available at arXiv:1501.07415 [math.FA]
• S. Bürger, J. Flemming: Deautoconvolution: A new decomposition approach versus TIGRA and local regularization, Journal of Inverse and III-posed Problems, 2015, volume 23, issue 3, pages 231-243, available online since 2014, DOI: 10.1515/jiip-2013-0082
• J. Flemming, M. Hegland: Convergence rates in l¹-regularization when the basis is not smooth enough, Applicable Analysis, 2015, volume 94, issue 3, pages 464-476, available online since 2014, DOI: 10.1080/00036811.2014.886106; earlier version available at arXiv:1311.1923v1 [math.NA]
• J. Flemming: Regularization of autoconvolution and other ill-posed quadratic equations by decomposition, Journal of Inverse and III-posed Problems, 2014, volume 22, issue 4, pages 551-567, available online since 2013, DOI: 10.1515/jip-2013-0038
• J. Flemming: Variational smoothness assumptions in convergence rate theory - an overview, Journal of Inverse and Ill-posed Problems, 2013, volume 21, issue 3, pages 395-409, DOI: 10.1515/jip-2013-0001
• M. Burger, J. Flemming, B. Hofmann: Convergence rates in l¹-regularization if the sparsity assumption fails, Inverse Problems, 2013, volume 29, issue 2, page 025013 (16 pp), DOI: 10.1088/0266-5611/29/2/025013
• S. Lu, J. Flemming: Convergence rate analysis of Tikhonov regularization for nonlinear ill-posed problems with noisy operators, Inverse Problems, 2012, volume 28, issue 10, page 104003 (20 pp), DOI: 10.1088/0266-5611/28/10/104003
• J. Flemming, B. Hofmann: Convergence rates in constrained Tikhonov regularization: equivalence of projected source conditions and variational inequalities, Inverse Problems, 2011, volume 27, issue 8, page 085001 (11 pp), DOI: 10.1088/0266-5611/27/8/085001
• J. Flemming: Solution smoothness of ill-posed equations in Hilbert spaces: four concepts and their cross connections, Applicable Analysis, 2012, volume 91, issue 5, pages 1029-1044; available online since 2011, DOI: 10.1080/00036811.2011.563736
• J. Flemming, B. Hofmann, P. Mathé: Sharp converse results for the regularization error using distance functions, Inverse Problems, 2011, volume 27, issue 2, page 025006 (18 pp), DOI: 10.1088/0266-5611/27/2/025006; earlier version: WIAS Preprint No. 1535, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, 2010, PDF file
• J. Flemming: Theory and examples of variational regularization with non-metric fitting functionals, Journal of Inverse and Ill-posed Problems, 2010, volume 18, issue 6, pages 677-699, DOI: 10.1515/jiip.2010.031; earlier version: Preprint series of the Department of Mathematics 2010-14, Chemnitz University of Technology, PDF file
• J. Flemming, B. Hofmann: A new approach to source conditions in regularization with general residual term, Numerical Functional Analysis and Optimization, 2010, volume 31, issue 3, pages 254-284, DOI: 10.1080/01630561003765721; earlier version available at arXiv:0906.3438v1 [math.NA]

Books

• J. Flemming: Data Science and Artificial Intelligence for Undergraduates, free online textbook, 2024, available online
• J. Flemming: Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization, Birkhäuser, Basel, 2018, ISBN 978-3-319-95263-5
• J. Flemming: Generalized Tikhonov regularization and modern convergence rate theory in Banach spaces, Shaker, Aachen, 2012, ISBN 978-3-8440-0867-8

Theses

• J. Flemming: Quadratic Inverse Problems and Sparsity Promoting Regularization. Two subjects, some links between them, and an application in laser optics, habilitation thesis, Chemnitz University of Technology, January 2018, PDF file (or permanent link)
• J. Flemming: Generalized Tikhonov regularization. Basic theory and comprehensive results on convergence rates, dissertation, Chemnitz University of Technology, October 2011, PDF file (or permanent link)
• J. Geissler (now J. Flemming): Untersuchungen zu Konvergenzraten bei der Tikhonov-Regularisierung mit allgemeinen Abstandsfunktionalen (Studies on convergence rates for Tikhonov regularization with general residual functionals), diploma thesis, Chemnitz University of Technology, June 2009, in German, corrected version (PDF)