Research

My research concentrates on evolution equations, operator semigroups and networks as part of functional analysis. Especially, I am interested in well-posedness of abstract Cauchy problems, extrapolation spaces and perturbation theory of operator semigroups. Non-strongly continuous operator semigroups are of special interest in this context. Furthermore, I participate in different research programs and stayed abroad for several research stays.

Publications

C. Budde, On bi-continuous cosine families, accepted to Quaest. Math. (2024)
C. Budde and C. Seifert, Perturbations of non-autonomous second-order abstract Cauchy problems, accepted to Anal. Math. (2024), arXiv:2302.11270.
C. Budde, A Banach bundle approach to dynamical processes on changing networks, accepted to Poincare J. Anal. Appl. (2024).
C. Budde and M. Kramar Fijavž, Well-posedness of non-autonomous transport equation on metric graphs, Semigroup Forum, 108:2, 319–334 (2024)
C. Budde and J. Kreulich, On Splittings and Integration of Almost Periodic Functions With and Without Geometry, Semigroup Forum, 108:2, 335–364 (2024)
C. Budde, How to approach stability of bi-continuous semigroups?, Math. Pannonica (N.S.), 29(2), 282-290 (2023)
C. Budde, On Trotter–Kato type inductive limits in the category of C0-semigroups, Adv. Dyn. Syst. Appl., 18:2, 125–136 (2023)
R. Benjamin, C. Budde, A note on the order Lozanovsky spectrum for positive operators, Complex Anal. Oper. Theory, 17:61 (2023)
C. Budde, A. Dobrick, J. Glück, M. Kunze, A monotone convergence theorem for strong Feller semigroups, Ann. Mat. Pura Appl. 202:1573-1589 (2023)
C. Budde, J. Kreulich, Application of abstract semigroup theory to the asymptotic behavior of C0-semigroups, Complex Anal. Oper. Theory, 16:105 (2022)
C. Budde, L. Labuschagne, C. Steyn, Almost everywhere convergence for noncommutative spaces, Banach J. Math. Anal., 16:56 (2022)
C. Budde, S.-A. Wegner, A Lumer-Phillips type generation theorem for bi-continuous semigroups, Z. Anal. Anwend. 41(1/2):65-80 (2022)
C. Budde, Perturbations of uniformly mean ergodic semigroups, J. Semigroup Theory Appl., 2021 (2021), Article ID 1
C. Budde, Positive Desch-Schappacher perturbations of bi-continuous semigroups on AM-spaces, Acta Sci. Math. (Szeged), 87(34):571–594 (2021)
C. Budde, M. Kramar Fijavz, Bi-continuous semigroups for flows in infinite networks, Netw. Heterog. Media, 16(4):553–567 (2021)
C. Budde, Semigroups for flows on limits of graphs, Univ. Iagel. Acta Math., 58:7–21 (2021)
C. Budde, Positive Miyadera–Voigt perturbations of bi-continuous semigroups, Positivity, 25(3): 1107–1129 (2021)
C. Budde, R. Heymann, Extrapolation of operator-valued multiplication operators, Quaest. Math., 45(3): 347–356 (2022)
C. Budde, B. Farkas, A Desch–Schappacher perturbation theorem for bi-continuous semigroups, Math. Nachr., 293(6):1053–1073 (2020)
C. Budde, B. Farkas, Intermediate and extrapolated spaces for bi-continuous operator semigroups, J. Evol. Equ. 19 (2019), no. 2, 321–359
C. Budde, K. Landsman, A bounded transform approach to self-adjoint operators: Functional calculus and affiliated von Neumann algebras, Ann. Funct. Anal. 7 (2016), no. 3, 411–420

Proceeding Articles

C. Budde, C. Seifert, Non-autonomous Desch-Schappacher perturbations, In: Choi, Y., Daws, M., Blower, G. (eds) Operators, Semigroups, Algebras and Function Theory. IWOTA 2021. Operator Theory: Advances and Applications, Vol 292. Birkhauser, Cham., 71–90 (2023)

Theses

General extrapolation spaces and perturbations of bi-continuous semigroups, Ph.D. thesis, Bergische Universität Wuppertal, 2019, Supervisor: Prof.Dr. Bálint Farkas, Second reader: Prof.Dr. Abdelaziz Rhandi, DOI:10.25926/7ss7-bt33
Operator algebras and unbounded self-adjoint operators, Master’s thesis, Radboud Universiteit Nijmegen, 2015, Supervisor: Prof.Dr. Klaas Landsman, Second reader: Dr. Jens Kaad, see here.
Representation of groups and their applications, Bachelor thesis, Radboud Universiteit Nijmegen, 2013, Original Dutch title: Representaties van groepen en hun Toepassingen, Supervisor: Prof.Dr. Gert Heckman, Second reader: Dr. Michael Müger.

Preprints

J. Allison, C. Budde, J. du Pisanie and J. Visagie, A critical review of existing and new population stability testing procedures in credit risk scoring, submitted, arXiv:2303.01227