Research Interests

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• Hilbert Space Operators, extension problems (Krein, Friedrichs etc.)
• Semigroups of Linear Operators, Abstract Cauchy problems
• Applications of operator matrix semigroups
• Damped wave equations
• Partial differential equations with delay
• Operator splitting, time discretiztion methods

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CV PDF-file

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Publications

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• Semigroups for delay equations (with S. Piazzera), monograph, A. K. Peters: Wellesley MA, Research Notes in Mathematics vol. 10,  ISBN: 1-56881-243-4, 2005.

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A.B., "Second Order Cauchy Problems with Damping and Delay", PhD Thesis, Tübingen, 2000. (ps-file)

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1. A.B., S. Piazzera, "Damped wave equations with delay", Fields Institute Communications 29(2001), 51-61.
2. A.B., S. Piazzera, "Semigroups and linear partial differential equations with delay", J. Math. Anal. Appl. 264(2001), 1-20. 
3. A.B., L. Maniar, A. Rhandi, "Regularity properties of perturbed Hille-Yosida operators and retarded differential equations", Semigroup Forum 64(2002), 55-70. 
4. A.B., S. Piazzera, "A semigroup method for delay equations with relatively bounded operators in the delay term", Semigroup Forum 64(2002), 71-89. 
5. Hyperbolicity of linear partial differential equations with delay, Int. Eq. Operator Theory 44 (2002), 383-396. 
6. A.B., E. Fasanga, R. Shvidkoy, "Hyperbolicity of delay equations via Fourier multipliers", Acta Sci. Math. (Szeged) 69 (2003), 131-145. 
7. A.B., B. Farkas, "On the effect of small delays to the stability of feedback systems", Progress in Nonlinear Differential Equations 55 (2003), 83-94. 
8. A. B, E. Fasanga, "The spectral mapping theorem for Davies' functional calculus", Rev. Roumaine Math. Pures Appl. 48 (2003), 365-372. 
9. On the domain characterization of fractional powers of certain operator matrices, Studia Sci. Math. Hung. 40 (2003), 327-340. 
10. A.B, K.J. Engel, "Abstract wave equations with generalized Wentzell boundary conditions", J. Diff. Eqs. 207 (2004), 1-20. 
11. A.B., R. Schnaubelt, "Asymptotic behaviour of parabolic problems with delays in the highest order derivatives", Semigroup Forum 69 (2004), 369-399. 
12. Semigroups for delay equations (with S. Piazzera, overview), International Minicourse-Workshop "Interplay between (C0)-semigroups and PDEs: theory and applications" (S. Romanelli, R.-M. Mininni, S. Lucente eds.), Arcane Editrice, Roma, 2004, pp. 1-54. (pdf file of 12/2/2004)
13. Spectral problems for operator matrices (with P. Binding, A. Dijksma, R. Hryniv and H. Langer), Math. Nachr. 278 (2005), 1408-1429. 
14. Cosine families generated by second order differential operators on W^1,1(0,1) with generalized Wentzell boundary conditions (with K.J. Engel and M. Haase), Applicable Analysis 84 (2005), 867-876. 
15. Exponential decay of 2x2 operator matrix semigroups (with K.J. Engel), J. Comp. Anal. Appl. 6 (2004), 153-164. [2006] 
16. Polynomial stability of operator semigroups (with K.J. Engel, J. Prüss and R. Schnaubelt), Math. Nachr. 279 (2006), 1425-1440. 
17. The spectral mapping property of delay semigroups (with Tanja Eisner and Yuri Latushkin), Complex Analysis and Operator Theory 2 (2008), 273-283.
18. Operator splittings and spatial approximations for evolution equations (with Petra Csomós and Gregor Nickel), J. Evol. Equations 9 (2009), 613-636. (doi:10.1007/s00028-009-0026-6)
19. Operator splitting for nonautonomous evolution equations (with Petra Csomós, Bálint Farkas, and Gregor Nickel), J. Funct. Anal. 260 (2011), 2163-2190. (doi:10.1016/j.jfa.2010.10.008)
20. The norm convergence of a Magnus expansion method (with Eszter Sikolya), Cent. Eur. J. Math. 10 (2012), 150-158. (doi: 10.2478/s11533-011-0101-4)
21. On shape preserving semigroups (with Adam Bobrowski), Arch. Math. 98 (2012), 37–48. (doi:10.1007/s00013-011-0340-4)
22. Decomposition of operator semigroups on W*-algebras (with U. Groh, D. Kunszenti-Kovács, M. Schreiber), Semigroup Forum 84 (2012), 8–24. (doi:10.1007/s00233-011-9362-2)
23. Operator splitting with spatial-temporal discretization (with Petra Csomós, Bálint Farkas, and Gregor Nickel), Operator Theory: Advances and Applications, 221 (2012), 161-171. (doi:10.1007/978-3-0348-0297-0_9)
24. Differential equation approximations of stochastic network processes: an operator semigroup approach (with Eszter Sikolya, István Z. Kiss, Péter L. Simon), Networks and Heterogeneous Media (NHM) 7 (2012), 43-58. (doi:10.3934/nhm.2012.7.43)
25. Operator splitting for nonautonomous delay equations (with Petra Csomós, Bálint Farkas), Computers & Mathematics with Applications, 2012. (doi:10.1016/j.camwa.2012.05.001)

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Preprints

Partly available at arXiv.

• Operátorfélcsoportok Polinomiális Stabilitása (pdf-file of 20/06/2005, in hungarian)

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Links

• Arbeitsgemeinschaft Funktionalanalysis Tübingen (Prof. Rainer Nagel)
• Institut für Analysis und Scientific Computing, TU Wien

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2^nd Dynamical Networks days, Genzano di Roma, 2005

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Research grants and prizes:

• Marie Curie postdoctoral research fellowship in the EU-Research Training Network HPRN-CT-2000-00116 "Analysis and Operators", 2001 (Vienna, Prof. Heinz Langer)
• "Gyula Farkas" prize of the János Bolyai Mathematical Society, 2003
• János Bolyai Research Fellowship of the Hungarian Academy of Sciences, 2004-2007
• OTKA Hungarian National Research grant F 049624 "Partial functional differential equations"
• Marie Curie postdoctoral research fellowship in the EU-Research Training Network HPRN-CT-2002-00281 "Evolution Equations", 2005 (Rome, Prof. Piermarco Cannarsa)
• Bolyai-Kelly Scholarship 2006
• Alexits György Prize oft he Hungarian Academy of Sciences, 2008
• Alexander von Humboldt-Stiftung, scholarship, 2009-2010.
• Alexander von Humboldt-Stiftung, return scholarship, 2011-2012.

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