Indagationes Mathematicae
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Volume II: Probabilistic Techniques and Operator Theory (Errata are available here (last update: 22.05.2024)) Volume III: Harmonic Analysis and Spectral Theory (Errata are available here (last update: 19.01.2024)) Volume IV: Stochastic Analysis (in preparation)
Edita:
Lecture Notes:Stochastic Evolution EquationsLecture notes of the Internet Seminar 2007/08 (version May 07, 2010) Papers:Downloadable files are preprint versions. They may differ at minor points from the published papers.MathematicsLévy measures on Banach spaces arxiv.org/pdf/2406.09362; submitted for publication Thermal time as an unsharp observable J. Math. Phys. 65 (2024), article 032105 Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices Comptes Rendus - Mathématique 361 (2023), 835-846 Maximal inequalities for stochastic convolutions and pathwise uniform convergence of time discretisation schemes Stoch. Partial Differ. Equ. Anal. Comput. 10 (2022), no 2, 516-581 Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions IMA J. Numer. Anal. 41 (2021), no 1, 493-548 The Weyl calculus for group generators satisfying the canonical commutation relations J. Operator Th. 83 (2020), no 2, 253-298 Maximal estimates for stochastic convolutions in 2-smooth Banach spaces and applications to stochastic evolution equations Philos. Trans. Roy. Soc. A 378 (2020), article 2185 Backward stochastic evolution equations in UMD Banach spaces In: "Positivity and Noncommutative Analysis, Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday" Trends in Mathematics, 2019, pp. 381-404 On conditional expectations in L^p(μ;L^q(ν;X)) Positivity 23 (2019), 11-19 The Weyl calculus with respect to the Gaussian measure and restricted L^p-L^q boundedness of the Ornstein-Uhlenbeck semigroup in complex time Bull. Soc. Math. France 146 (2018), no 4, 691-712 L^p-Analysis of the Hodge--Dirac operator associated with Witten Laplacians on complete Riemannian manifolds J. Geom. Anal. 28 (2018), no. 4, 3109-3138 Finite speed of propagation and off-diagonal bounds for Ornstein-Uhlenbeck operators in infinite dimensions Annali Mat. Pura Appl. 195 (2016), 1889-1915 On the constant in a transference inequality for the vector-valued Fourier transform Austral. J. Math. Anal. Appl. 13 (1), Article 2, pp. 1-11, 2016 MR 3 505 504 Stochastic integration in Banach spaces - a survey In: "Stochastic Analysis: A Series of Lectures" (Lausanne, 2012) Progress in Probability, Vol. 68, Birkhäuser Verlag, 2015 The L^p-Poincaré inequality for analytic Ornstein-Uhlenbeck operators In: "Operator Semigroups meet Complex Analysis, Harmonic Analysis and Mathematical Physics" (Hernnhut, 2013) Operator Theory: Advances and Applications, Vol. 250, Birkhäuser Verlag, Basel, 2015 MR 3 496 370 Maximal γ-regularity J. Evol. Equ. 15 (2015), no. 2, 361-402 MR 3 353 141 Second quantisation for skew convolution products of infinitely divisible measures Infin. Dimens. Anal. Quantum Probab. Relat. Top. 18 (2015), no. 1, paper 1550003 MR 3 324 719 On the R-boundedness of stochastic convolution operators Positivity 19 (2015), 355-384 MR 3 357 999 Conical stochastic maximal L^p-regularity for 1 ≤ p < ∞ Math. Ann. 359 (2014), no. 3, 863-889 MR 3 231 019 Second quantisation for skew convolution products of measures in Banach spaces Electron. J. Probab. 19 (2014), paper 11, 1-17 MR 3 164 764 Compactness in the Lebesgue-Bochner spaces L^p(μ;X) Indag. Math. 25 (2014), no. 2, 389-394 MR 3 151 824 Poisson stochastic integration in Banach spaces Electron. J. Probab. 18 (2013), paper 100, 1-28 MR 3 141 801 Pathwise Hölder convergence of the implicit Euler scheme for semi-linear SPDEs with multiplicative noise Numerische Mathematik 125 (2013), no. 2, 259-345 MR 3 101 829 The stochastic Weiss conjecture for bounded analytic semigroups J. London Math. Soc. 88 (2013), no. 1, 181-201 MR 3 092 264 Equivalence of laws and null controllability for SPDEs driven by a fractional Brownian motion NoDEA 20 (2013), no. 4, 1473-1498 MR 3 078 239 L^2-Theory for non-symmetric Ornstein-Uhlenbeck semigroups on domains J. Evol. Equ. 13 (2013), no. 1, 107-134 MR 3 020 139 Uniformly γ-radonifying families of operators and the stochastic Weiss conjecture Operators and Matrices 6 (2012), no. 4, 767-792 MR 3 025 035 Whitney coverings and the tent spaces T^{1,q}(γ) for the Gaussian measure Arkiv för Matematik 50 (2012), 379-395 MR 2 961 328 Maximal L^p-regularity for stochastic evolution equations SIAM J. Math. Anal. 44 (2012), no. 3, 1372-1414 MR 2 982 717 Continuous dependence on the coefficients and global existence for stochastic reaction-diffusion equations J. Differential Equations 253 (2012), 1036-1068 MR 2 922 662 Stochastic maximal L^p-regularity Ann. Probab. 40 (2012), 788-812 MR 2 952 092 Stochastic evolution equations driven by Liouville fractional Brownian motion Czech. Math. J. 62 (2012), 1-27 MR 2 899 731 A maximal inequality for stochastic convolutions in 2-smooth Banach spaces Electron. Commun. Probab. 16 (2011), 689-705 MR 2 861 433 Non-tangential maximal functions and conical square functions with respect to the Gaussian measure Pub. Mat. 55 (2011), 313-341 MR 2 839 445 Approximating the coefficients in semilinear stochastic partial differential equations J. Evol. Equ. 11 (2011), 577-604 MR 2 827 101 Gradient estimates and domain identification for analytic Ornstein-Uhlenbeck operators In: "Parabolic Problems: The Herbert Amann Festschrift" Progress in Nonlinear Differential Equations and Their Applications, Vol. 80, Birkhäuser Verlag, 2011, 463-477 MR 3 052 592 A remark on the factorization method In: "Stochastic Partial differential Equations and Applications" (Levico Terme, 2008) Quaderni di Matematica, Vol. 25, Universita di Napoli, 2010, 257-270 MR 2 985 092 γ-Radonifying operators - a survey Proceedings of the CMA 44 (2010), 1-62 MR 2 655 391 Convergence rates of the splitting scheme for parabolic linear stochastic Cauchy problems SIAM J. Numer. Anal. 48 (2010), 428-451 MR 2 646 103 Spaces of operator-valued functions measurable with respect to the strong operator topology In: Vector Measures, Integration and Applications (Eichstätt, 2008) Operator Theory: Advances and Applications, Vol. 201, Birkhäuser, 2010, 65--78 MR 2 743 975 Vector measures of bounded γ-variation and stochastic integrals In: "Vector Measures, Integration and Applications" (Eichstätt, 2008) Operator Theory: Advances and Applications, Vol. 201, Birkhäuser, 2010, 303--312 MR 2 743 996 Boundedness of Riesz transforms for elliptic operators on abstract Wiener spaces J. Funct. Anal. 257 (2009), 2410-2475 MR 2 555 015 Asymptotic behaviour of C_0-semigroups and γ-boundedness of the resolvent J. Math. Anal. Appl. 358 (2009), 380-388 MR 2 532 514 On the domain of nonsymmetric Ornstein-Uhlenbeck operators in Banach spaces Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11 (2008), 603-626 MR 2 483 799 Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi J. Analyse Math. 106 (2008), 317-351 MR 2 448 989 Stochastic evolution equations in UMD Banach spaces J. Funct. Anal. 255 (2008), 940-993 MR 2 433 958 Stochastic integration of operator-valued functions with respect to Banach space-valued Brownian motion Potential Anal. 29 (2008), 65-88 MR 2 421 495 Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation J. Differential Equations 245 (2008), 30-58 MR 2 422 709 A Clark-Ocone formula in UMD Banach spaces Electron. Comm. Probab. 13 (2008), 151-164 MR 2 399 277 Embedding vector-valued Besov spaces into spaces of gamma-radonifying operators Math. Nachr. 281 (2008), 238-252 MR 2 387 363 Conditions for stochastic integrability in UMD Banach spaces In: "Banach Spaces and their Applications in Analysis: In Honor of Nigel Kalton's 60th Birthday" De Gruyter Proceedings in Mathematics, De Gruyter, 2007, 127-146 MR 2 374 704 On analytic Ornstein-Uhlenbeck semigroups in infinite dimensions Archiv Math. (Basel) 89 (2007), 226-236 MR 2 352 390 Compactness in vector-valued Banach function spaces Positivity 11 (2007), 461-467 MR 2 336 209 Stochastic integration in UMD Banach spaces Ann. Probab. 35 (2007), 1438-1478 MR 2 330 977 A semigroup approach to stochastic delay equations in spaces of continuous functions Semigroup Forum 74 (2007), 227-239 MR 2 312 964 A stochastic Datko-Pazy theorem J. Math. Anal. Appl. 329 (2007), 1230-1239 MR 2 296 921 Continuity versus nonexistence for a class of linear stochastic Cauchy problems driven by a Brownian motion Czech. Math. J. 56 (131) (2006), 579-586 MR 2 291 757 Space-time regularity of solutions of the parabolic stochastic Cauchy problem Stoch. Anal. Appl. 24 (2006), 843-869 MR 2 241 096 Invariant measures for the linear stochastic Cauchy problem and R-boundedness of the resolvent J. Evol. Equ. 6 (2006), 205-228 MR 2 227 694 Invariant measures for stochastic Cauchy problems with asymptotically unstable drift semigroup Electron. Commun. Probab. 11 (2006), 24-34 MR 2 211 424 On the stochastic Fubini theorem in infinite dimensions In: "Stochastic Partial Differential Equations and Applications - VII" (Levico Terme, 2004) Lecture Notes in Pure and Applied Mathematics, Volume 245, Chapman & Hall/CRC, 2005, 323-336 MR 2 227 239 Weak limits and integrals of Gaussian covariances in Banach spaces Probab. Math. Statist. 25 (2005), 55-74 MR 2 211 356 Norm discontinuity and spectral properties of Ornstein-Uhlenbeck semigroups J. Evol. Equ. 5 (2005), 557-576 MR 2 201 527 Second quantization and the L^p-spectrum of nonsymmetric Ornstein-Uhlenbeck operators Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8 (2005), 473-496 MR 2 172 310 On the action of Lipschitz functions on vector-valued random sums Archiv Math. (Basel) 85 (2005), 544-553 MR 2006i:46013 Separated sequences in uniformly convex Banach spaces Colloq. Math. 102 (2005), 147-153 MR 2005m:46023 Null controllability and the algebraic Riccati equation in Banach spaces SIAM J. Control Optim. 43 (2005), 1313-1327 MR 2005k:93021 Stochastic integration of functions with values in a Banach space Studia Math. 166 (2005), 131-170 MR 2005j:60107 A Lie-Trotter product formula for Ornstein-Uhlenbeck semigroups in infinite dimensions J. Evol. Equ. 4 (2004), 53-73 MR 2004m:60139 Space-time regularity for linear stochastic evolution equations driven by spatially homogeneous noise J. Math. Kyoto Univ. 43 (2003), 275-317 MR 2005c:60077 Mean square continuity of Ornstein-Uhlenbeck processes in Banach spaces In: "Evolution Equations 2000" (Levico Terme, 2000) Progr. Nonlinear Differential Equations Appl., Vol.55, Birkhäuser, 2003, 97-102 MR 2004k:60161 Transition semigroups of Banach space valued Ornstein-Uhlenbeck processes Acta Appl. Math. 76 (2003), 283-330 (Revised version) MR 2004b:47075 On closability of directional gradients Potential Anal. 18 (2003), 289-310 MR 2004a:60107 Approximating Bochner integrals by Riemann sums Indag. Math. N.S. 13 (2002), 197-208 MR 2004j:28020 Lower semicontinuity and the theorem of Datko and Pazy Integral Equations Operator Theory 42 (2002), 482-492 MR 2003i:47044 On individual stability of C_0-semigroups Proc. Amer. Math. Soc. 130 (2002), 2325-2333 MR 2003a:47094 Uniqueness of invariant measures for the stochastic Cauchy problem in Banach spaces In: "Recent Advances in Operator Theory and Related Topics: The Béla Szökefalvi-Nagy Memorial Volume" Operator Theory: Advances and Applications, Vol. 127, Birkhäuser, 2001, 491-517 MR 2003d:60115 Banach space valued Ornstein-Uhlenbeck processes indexed by the circle In: "Evolution Equations and their Applications in Physical and Life Sciences" (Bad Herrenalb, 1998) Lecture Notes in Pure and Applied Mathematics, Vol. 215, Marcel Dekker, 2000, 435-452 MR 2002e:60052 The vector-valued Loomis theorem for the half-line and individual stability of C_0-semigroups: a counterexample Semigroup Forum 60 (2000), 271-283 MR 2002b:47082 Continuity and representation of Gaussian Mehler semigroups Potential Anal. 13 (2000), 199-211 MR 2002a:47066 Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem Studia Math. 143 (2000), 43-74 MR 2001m:60143 Asymptotic behaviour of C_0-semigroups with bounded local resolvents Math. Nachr. 219 (2000), 65-83 MR 2001i:47065 Equivalence of Banach space-valued Ornstein-Uhlenbeck processes Stoch. Stoch. Reports 69 (2000), 77-94 MR 2000m:60039 Norm discontinuity of Ornstein-Uhlenbeck semigroups Semigroup Forum 59 (1999), 389-403 MR 2002g:47090 Sandwiching C_0-semigroups J. London Math. Soc. 60 (1999), 581-588 MR 2000g:47049 B-convexity, the analytic Radon-Nikodym property, and individual stability of C_0-semigroups J. Math. Anal. Appl. 231 (1999), 1-20 MR 2000i:47077 On the existence and growth of mild solutions of the abstract Cauchy problem for operators with polynomially bounded resolvent Houston J. Math. 24 (1998), 137-172 MR 2001a:34103 The norm of a complex Banach lattice Positivity 1 (1998), 383-392 MR 2000j:46035 Nonsymmetric Ornstein-Uhlenbeck semigroups in Banach spaces J. Funct. Anal. 155 (1998), 495-535 MR 99h:60083 Robust stability of C_0-semigroups and an application to stability of delay equations J. Math. Anal. Appl. 226 (1998), 82-100 MR 99g:47092 On small solutions of delay equations in infinite dimensions Integral Equations Operator Theory 31 (1998), 178-185. MR 99c:34181 Ditkin's condition for certain Beurling algebras Proc. Amer. Math. Soc. 126 (1998), 1397-1407 MR 98k:43009 Tauberian theorems and stability of solutions of the Cauchy problem Trans. Amer. Math. Soc. 350 (1998), 2087-2103 MR 98h:47055 Local spectra and individual stability of uniformly bounded C_0-semigroups Trans. Amer. Math. Soc. 350 (1998), 2071-2085 MR 98h:47054 Elementary operator-theoretic proof of Wiener's Tauberian theorem Rendic. Istit. Matem. Univ. Trieste., Suppl. Vol. XXVIII (1997), 281-286 MR 99a:47058 Polynomially bounded operators whose spectrum on the unit circle has measure zero Acta Sci. Math. (Szeged) 63 (1997), 559-570 MR 99a:47007 Individual stability of C_0-semigroups with uniformly bounded local resolvent Semigroup Forum 53 (1996), 155-161 MR 97h:47036 Inequality of spectral bound and growth bound for positive semigroups in rearrangement invariant Banach function spaces Arch. Math. (Basel) 66 (1996), 406-416 MR 97c:47046 Characterization of exponential stability of a semigroup of operators in terms of its action by convolution on vector-valued function spaces over R_+ J. Differential Equations 124 (1996), 324-342 MR 96k:47074 On the asymptotic behaviour of a semigroup of linear operators Indag. Math. (N.S.) 6 (1995), 453-476 MR 96k:47073 Weak measurability of the orbits of an adjoint semigroup In: "Evolution Equations" (Baton Rouge, LA, 1992) Lecture Notes in Pure and Appl. Math., Vol. 168, Marcel Dekker, 1995, 327-336 MR 95h:47058 On the orbits of an operator with spectral radius one Czechoslovak Math. J. 45 (120) (1995), 495-502 MR 96f:47009 Exponential stability of operators and operator semigroups J. Funct. Anal. 130 (1995), 293-309 MR 96f:47006 Remark on a theorem of Riddle, Saab, and Uhl Quaestiones Math. 17 (1994), 183-187 MR 95e:46058 The adjoint of a positive semigroup Compositio Math. 90 (1994), 99-118 MR 95b:47048 Abstract multiplication semigroups Math. Z. 213 (1993), 1-15 MR 94e:47052 Some recent results on adjoint semigroups CWI Quarterly 6 (1993), 139-153 MR 94e:47051 A dichotomy theorem for the adjoint of a semigroup of operators Proc. Amer. Math. Soc. 119 (1993), 765-774 MR 93m:47044 Adjoints of semigroups acting on vector-valued function spaces Israel J. Math. 77 (1992), 305-333 MR 94f:47043 A converse of Lotz's theorem on uniformly continuous semigroups Proc. Amer. Math. Soc. 116 (1992), 525-527 MR 92m:47077 Reflexivity, the dual Radon-Nikodym property, and continuity of adjoint semigroups II Indag. Math. (N.S.) 2 (1991), 243-250 MR 93f:47047 On the topology induced by the adjoint of a semigroup of operators Semigroup Forum 43 (1991), 378-394 MR 93e:47049 Certain semigroups on Banach function spaces and their adjoints In: Semigroup Theory and Evolution Equations (Delft, 1989) Lecture Notes in Pure and Appl. Math., Vol. 135, Marcel Dekker, 1991, 383-390 MR 93d:47078 Reflexivity, the dual Radon-Nikodym property, and continuity of adjoint semigroups Indag. Math. (N.S.) 1 (1990), 365-379 MR 92k:46019 Hahn-Banach type theorems for adjoint semigroups Math. Ann. 287 (1990), 63-71 MR 91e:47042 PhysicsDelayed choice experiments: An analysis in forward time Quantum Studies: Mathematics and Foundations, Online First, 2024 Relational analysis of the Frauchiger--Renner paradox and interaction-free detection of records from the past Foundations of Physics, Article number 45 (2021) The Garrison-Wong quantum phase operator revisited arXiv:2008.08935 BiologyChaos or noise in EEG signals; dependence on state and brain site Electroenceph. and Clin. Neurophys. 79 (1991), 371-381 Cellular and network mechanisms in the kindling model of epilepsy: the role of GABA-ergic inhibition and the emergence of strange attractors In: "Machinery of the Mind", Chapter 6, Birkhäuser, Basel, 1990, 115-139 Recreational and outreachWigner's `unreasonable effectiveness of mathematics' as a philosophical problem In: "Mathematisches Denken", Proceedings of the Rom Seminar 2017 Filosofie van de Wiskunde - een impressie MaCHazine 20 (1) 2015, 40-41 (in Dutch) Stochastische integratie in Banachruimten Nieuw Archief voor Wiskunde 5/15 2014 (3), 180-187 (in Dutch) De KPZ-vergelijking Nieuw Archief voor Wiskunde 5/15 2014 (1), 37-39 (in Dutch) MR 3 222 491 Op sabbatical MaCHazine 18 (3) 2014, 24-25 (in Dutch) Infinite Dimensions (Inaugural lecture, in Dutch) Nieuw Archief voor Wiskunde 10 (2009), no. 1, 22-28 Van Fourier transformaties tot stochastische differentiaalvergelijkingen MaCHazine 12 (4) 2008, 32-34 (in Dutch) De wiskunde van kleurplaten MaCHazine 7 (2) 2003, 12-15 (in Dutch)
The nature of fractal geometry CWI Quarterly 3 (1990), 137-149 MR 91j:58091 Several elementary proofs that 0=1 Nieuw Archief voor Wiskunde, 4e Serie, Deel 8 (1990), 253-256 |