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Institute for Analysis
Workgroup Applied Analysis
apl. Prof. Dr. Peer Christian Kunstmann
publications

Publications Kunstmann

Publications Peer Christian Kunstmann


Book Chapter

(with L. Weis) Maximal L_p-regularity for parabolic equations, Fourier multiplier theorems and H^\infty-calculus, in Functional Analytic Methods for Evolution Equations (eds. M. Iannelli, R. Nagel and S. Piazzera), Springer Lecture Notes 1855, 65-311 (2004).

Submitted Papers

  • G. Herzog, P.C. Kunstmann: Minimal periods for semilinear parabolic equations, to appear in Archiv der Mathematik.
  • H. Kozono, P.C. Kunstmann, S. Shimizu: Generalized quasi-geostrophic equation in the critical Lorentz-Besov space based on the maximal regularity theorem.
  • H. Kozono, P. Kunstmann, S. Shimizu: Analyticity in space-time of solutions to the Navier-Stokes equations via parameter trick based on maximal regularity, to appear in Ann. Sc. Norm. Sup. Pisa.
  • S. Bechtel, C. Bui, P.C. Kunstmann: Around maximal regularity for Navier-Stokes equations, Panoramas et Synthèses 61, 2024, p. 29-76, to appear.

Published Papers

  1. G. Herzog, P.C. Kunstmann: Eventually positive elements in ordered Banach algebras, Comment. Math. Univ. Carolin. 64 (2023), no. 3, 321–330.
  2. P.C. Kunstmann, E.T. Quinto, A. Rieder: Seismic imaging with generalized Radon transforms: stability of the Bolker condition, Pure Appl. Math. Q. 19 (2023), no. 4, 1985--2036. Preprint.
  3. G. Herzog, P.C. Kunstmann: A weak differential inequality, Publ. Math. Debrecen 102/1-2 (2023), 255–259.
  4. D. Hundertmark, P. Kunstmann, T. Ried, S. Vugalter: Cwikel's bound reloaded. Invent. Math. 231 (2023), no. 1, 111–167. Preprint. on arxiv.org.
  5. F. Klaus, P. Kunstmann: Global wellposedness of NLS in . J. Math. Anal. Appl. 514 (2022) 126359. Preprint. on arxiv.org.
  6. G. Herzog, P.C. Kunstmann: Spectral symmetry of solutions of boundary value problems in Banach algebras. Annales Polonici Matematici 128.1 (2022), 39-48.
  7. D. Hundertmark, P. Kunstmann, T. Ried, S. Vugalter: Counting bound states with maximal Fourier multipliers. in Partial differential equations, spectral theory, and mathematical physics—the Ari Laptev anniversary volume, 197–207, EMS Ser. Congr. Rep., EMS Press, Berlin, 2021.
  8. P.C. Kunstmann: On continuity properties of semigroups in real interpolation spaces. J. Evol. Equ. 21 (2021), no. 3, 3503–3520.
  9. G. Herzog, P.C. Kunstmann: Quadratic inequalities for functionals in , Opuscula Math. 41 (2021), no. 3, 437–446.
  10. F. Klaus, P.C. Kunstmann, N. Pattakos: Unconditional uniqueness of higher order nonlinear Schrödinger equations, Czechoslovak Math. J. 71(146) (2021), no. 3, 709–742. Preprint; on arxiv.org.
  11. L. Chaichenets, D. Hundertmark, P. Kunstmann, N. Pattakos: On the global well-posedness of the quadratic NLS on , NoDEA Nonlinear Differential Equations Appl. 28 (2021), no. 2, Paper No. 11. Preprint; on arxiv.org.
  12. L. Chaichenets, D. Hundertmark, P.C. Kunstmann, N. Pattakos: Local Well-Posedness for the Nonlinear Schrödinger Equation in the Intersection of Modulation Spaces M^s_{p,q}(\R^d)\cap M_{\infty,1}(\R^d). In: , et al. Mathematics of Wave Phenomena, pp. 89-107, Trends in Mathematics. Birkhäuser, Cham, 2020. https://doi.org/10.1007/978-3-030-47174-3_6.
  13. G. Herzog, P.C. Kunstmann: Asymptotic constants in averaged Hölder inequalities, Real Anal. Exchange 45 (2020), no. 2, 425–437.
  14. C. Grathwohl, P.C. Kunstmann, E.T. Quinto, A. Rieder: Imaging with the elliptic Radon transform in three dimensions from an analytical and numerical perspective, SIAM J. Imaging Sci. 13 (2020), no. 4, 2250–2280. Preprint.
  15. L. Chaichenets, D. Hundertmark, P.C. Kunstmann, N. Pattakos: Knocking out teeth in one-dimensional periodic nonlinear Schrödinger equation, SIAM J. Math. Anal. 51 (2019), no. 5, 3714–3749. Preprint; on arxiv.org.
  16. L. Chaichenets, D. Hundertmark, P.C. Kunstmann, N. Pattakos: Nonlinear Schrödinger equation, differentiation by parts and modulation spaces, J. Evol. Equ. 19 (2019), no. 3, 803–843. Preprint.
  17. G. Herzog, P.C. Kunstmann: Korovkin's theorem for functionals and limits for box integrals, Amer. Math. Monthly 126 (2019), no. 5, 449–454.
  18. P.C. Kunstmann: Modulation type spaces for generators of polynomially bounded groups and Schrödinger equations, Semigroup Forum 98, no. 3, 645–668 (2019). (Preprint)
  19. G. Herzog, P.C. Kunstmann, Boundary value problems with solutions in convex sets, Opuscula Math. 39(1), 49-60 (2019).
  20. P.C. Kunstmann, Buyang Li, C. Lubich: Runge-Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity, Found. Comput. Math. 18 (2018), no. 5, 1109–1130.
  21. C. Grathwohl, P.C. Kunstmann, E.T. Quinto, A. Rieder: Microlocal Analysis of Imaging Operators for Effective Common Offset Seismic Reconstruction, Inverse Problems 34(11), 114001 (2018).
  22. J. Babutzka, P.C. Kunstmann, -Helmholtz decomposition on periodic domains and applications to Navier-Stokes equations, J. Math. Fluid Mech. 20(3), 1093-1121 (2018).
  23. C. Grathwohl, P.C. Kunstmann, E.T. Quinto, A. Rieder, Approximate inverse for the common offset acquisition geometry in 2D seismic imaging, Inverse Problems 34(1), 014002, 25 pp. (2018).
  24. L. Caichenets, D. Hundertmark, P. Kunstmann, N. Pattakos: On existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space M_{p,q}(\mathbb R), J. Differential Equations 263(8), 4429-4441 (2017). Preprint
  25. G. Herzog, P.C. Kunstmann: Two applications of a generalization of an asymptotic fixed point theorem, Order 34(2), 323-326 (2017).
  26. G. Herzog, P.C. Kunstmann: A note on vector translation with respect to Thompson's metric, Numerical Functional Analysis and Optimization 38(8), 1008-1013 (2017).
  27. P.C. Kunstmann, L. Weis: New criteria for the -calculus and the Stokes operator on bounded Lipschitz domains, Journal of Evolution Equations 17(1), 387-409 (2017).
  28. M. Haase, P.C. Kunstmann, H. Vogt: On the numerical range of generators of symmetric L_\infty-contractive semigroups, Archiv der Mathematik 107(5), 553–559 (2016). Preprint arXiv: 1603.08862
  29. P.C. Kunstmann: A new interpolation approach to spaces of Triebel-Lizorkin type, Illinois J. Math. 59 (2015), no. 1, 1–19. (Preprint).
  30. G. Herzog, P.C. Kunstmann: Asymptotic estimates in Thompson's metric for semilinear parabolic equations, Nonlinear Analysis: Theory, Methods & Applications 131, 112-120 (2016).
  31. P.C. Kunstmann, A. Ullmann: R_s-bounded H^\infty-calculus for sectorial operators via generalized Gaussian estimates, Mathematische Nachrichten 288 (11-12), 1371-1387 (2015).
  32. G. Herzog, P.C. Kunstmann: Universally divergent Fourier series via Landau’s extremal functions, Commentationes Mathematicae Universitatis Carolinae 56 (2), 159-168 (2015).
  33. P.C. Kunstmann, M. Uhl: Spectral Multiplier Theorems of Hörmander Type on Hardy and Lebesgue Spaces, Journal of Operator Theory 73 (1), 27-69 (2015). Preprint arXiv:1209.0358v1
  34. D. Hundertmark, P.C. Kunstmann, R. Schnaubelt: Stability of dispersion managed solitons for vanishing average dispersion, Archiv der Mathematik 104 (3), 283-288 (2015).
  35. M. Geißert, P.C. Kunstmann: Weak Neumann implies H^\infty for Stokes, Journal Math. Soc. Japan 67 (no. 1), 183-193 (2015).
  36. P.C. Kunstmann, M. Uhl: L^p-spectral multipliers for some elliptic systems, Proceedings of the Edinburgh Mathematical Society 58 (no. 1) 231-253 (2015). Preprint arXiv:1209.0694v1
  37. G. Herzog, P.C. Kunstmann: Global asymptotic stability for semilinear equations via Thompson's metric, Extracta Mathematicae 29 (Núm. 1-2) 141–157 (2014).
  38. G. Herzog, P.C. Kunstmann: A local Landau type inequality for semigroup orbits, Studia Math. 223(1), 19-26 (2014).
  39. G. Herzog, P.C. Kunstmann: Kuratowski's measure of noncompactness with respect to Thompson's metric, Zeitschrift für Analysis und ihre Anwendungen/Journal of Analysis and its Applications 33, 335-346 (2014).
  40. G. Herzog, P.C. Kunstmann: Inequalities and Means from a Cyclic Differential Equation, Demonstr. Math. 47 (no. 2) 300–309 (2014).
  41. P.C. Kunstmann, A. Ullmann: R_s-sectorial operators and generalized Triebel-Lizorkin spaces, Journal of Fourier Analysis and Applications 20 (no. 1) 135-185 (2014). Preprint: arXiv:1207.4217v1
  42. P. Kunstmann, L. Weis: Erratum to: Perturbation and interpolation theorems for the H^\infty-calculus with applications to differential operators, Mathematische Annalen 357 (no. 2), 801-804 (2013).
  43. D. Frey, P.C. Kunstmann: A T(1)-Theorem for non-integral operators, Mathematische Annalen 357 (no. 1), 215-278 (2013). Preprint: arXiv:1107.4347v1
  44. G. Herzog, P.C. Kunstmann: A fixed point theorem for decreasing functions, Numerical Functional Analysis and Optimization 34(5), 530-538 (2013).
  45. Navier-Stokes equations on unbounded domains with rough initial data, Czechoslovak Math. J. 60(135) no. 2, 297–313 (2010).
  46. (with Lizhen Ji and Andreas Weber) Riesz Transform on Locally Symmetric Spaces and Riemannian Manifolds with a Spectral Gap, Bulletin des Sciences Mathématiques 134, no. 1, 37-43 (2010).
  47. (with B. Haak) On Kato's method for Navier-Stokes equations, Journal Math. Fluid Mech. 11, 492-535 (2009).
  48. On maximal regularity of type L^p-L^q under minimal assumptions for elliptic non-divergence operators, Journal Functional Analysis 255, No. 10, 2732-2759 (2008).
  49. H^\infty-calculus for the Stokes operator on unbounded domains, Archiv Math. 91, 178-186 (2008).
  50. (with M. Mijatovic and S. Pilipovic) Classes of distribution semigroups, Stud. Math. 187, 37-58 (2008).
  51. Post-Widder inversion for Laplace transforms of hyperfunctions, in H. Amann, W. Arendt, M. Hieber, S. Nicaise, J. von Below (eds): Functional Anaylsis and Evolution Equations. The Günter Lumer Volume, Birkhäuser 2007, 423-431.
  52. (with H. Vogt) Weighted norm estimates and L_p-spectral independence of linear operators, Colloq. Math. 109, 129-146 (2007).
  53. (with B. Haak) Weighted admissibility and wellposedness of linear systems in Banach spaces, SIAM J. Control Optimization 45, 2094-2118 (2007).
  54. (with N.J. Kalton and L. Weis) Perturbation and interpolation theorems for the H^\infty-calculus with applications to differential operators, Mathematische Annalen 336, 747-801 (2006).
  55. (with B. Haak) Admissibility of unbounded operators and wellposedness of linear systems in Banach spaces, Integral Equations and Operator Theory 55, 497-533 (2006).
  56. (with G. Herzog) Majorization of C_0-semigroups in ordered Banach spaces, Commentationes Math. Univ. Carolinae 47 (1), 47-54 (2006).
  57. (with B. Haak and M. Haase) Perturbation, interpolation, and maximal regularity, Adv. Differential Equations 11 (2), 201-240 (2006).
  58. On elliptic non-divergence operators with measurable coefficients, Progress in Nonlinear Differential Equations and Their Applications, Vol. 64, 265-272, Birkhäuser 2005.
  59. (with S. Blunck) Generalized Gaussian estimates and the Legendre transform, J. Operator Theory 53, 351-365 (2005).
  60. (with S. Blunck) Weak type (p,p) estimates for Riesz transforms, Math. Z. 247, 137-148 (2004).
  61. (with S. Blunck) Calderon-Zygmund theory for non-integral operators and the H^\infty-calculus, Revista Mat. Iberoam. 19, 919-942 (2003).
  62. Maximal L_p-regularity for second order operators with uniformly continuous coefficients on domains, Progress in Nonlinear Differential Equations and Their Applications, Vol. 55, 293-305, Birkhäuser 2003.
  63. (with Z. Strkalj) H^\infty-calculus for submarkovian generators, Proc. Amer. Math. Soc. 131, 2081-2088 (2003).
  64. (with S. Blunck) Weighted norm estimates and maximal regularity, Adv. Differential Equations 7 (12), 1513-1532 (2002).
  65. L_p-spectral properties of the Neumann Laplacian on horns, comets and stars, Math. Z. 242, 183-201 (2002).
  66. Uniformly elliptic operators with maximal L_p-spectrum in planar domains, Arch. Math. 76, 377-384 (2001).
  67. Nonuniqueness and wellposedness of abstract Cauchy problems in a Frechet space, Bull. Austr. Math. Soc. 63, 123-131 (2001).
  68. (with L. Weis) Perturbation theorems for maximal L_p-regularity, Ann. Sc. Norm. Sup. Pisa 30, 415-435 (2001).
  69. (with G. Herzog) Stability for families of positive semigroups and partial differential equations via one-sided estimates, Demonstratio Math. 34 (1), 77-82 (2001).
  70. Laplace transform theory for logarithmic regions, Lumer, G., Weis, L. (Ed.) Evolution equations and their applications in physical and life sciences, Proceedings of the 6th international conference. Bad Herrenalb (Karlsruhe), September 1998. Marcel Dekker, 125-138 (2001).
  71. Kernel estimates and L^p-spectral independence of differential and integral operators, Gheondea, A. (Ed.) et al., Operator theoretical methods, Proceedings of the 17th international conference on operator theory, Timisoara, Romania, June 23-26, 1998. Bucharest: The Theta Foundation. 197-211 (2000).
  72. Spectral inclusions for semigroups of closed operators, Semigroup Forum 60, No.2, 310-320 (2000).
  73. Heat kernel estimates and L^p spectral independence of elliptic operators, Bull. Lond. Math. Soc. 31, No.3, 345-353 (1999).
  74. Distribution semigroups and abstract Cauchy problems, Trans. Am. Math. Soc. 351, No.2, 837-856 (1999).
  75. Regularization of semigroups that are strongly continuous for t>0, Proc. Am. Math. Soc. 126, No.9, 2721-2724 (1998).
  76. Stationary dense operators and generation of non-dense distribution semigroups, J. Oper. Theory 37, No.1, 111-120 (1997).


Habilitation Thesis

L_p-spectral properties of elliptic differential operators, Habilitationsschrift, Universität Karlsruhe (TH), Fakultät für Mathematik, 2002.

Doctoral Thesis

Abstrakte Cauchyprobleme und Distributionshalbgruppen, Dissertation, Universität Kiel, Mathematisch-Naturwissenschaftliche Fakultät, 1995.