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Department of Mathematics

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Institutes

Institute for Analysis

Workgroup Functional Analysis

Prof. Dr. Lutz Weis

Prof. Dr. Lutz Weis

Publications

Books and Book chapters

Tuomas Hytönen, Jan van Neerven, Mark Veraar, and Lutz Weis, Analysis in Banach Spaces (in preparation)

Peer C. Kunstmann and Lutz Weis, Maximal $L_p$ -regularity for parabolic equations, Fourier multiplier theorems and $H^\infty$ -functional calculus, Functional analytic methods for evolution equations, Lecture Notes in Math., vol. 1855, Springer, Berlin, 2004, pp. 65--311.

Günter Lumer and Lutz Weis (eds.), Evolution equations and their applications in physical and life sciences, Lecture Notes in Pure and Applied Mathematics, vol. 215, New York, Marcel Dekker Inc., 2001.

Articles

Jan van Neerven, Mark Veraar, and Lutz Weis, Stochastic maximal $L_p$ -regularity, Annals of Probability,(to appear).

Jan van Neerven, Mark Veraar, and Lutz Weis, Maximal $L^p$ -regularity for stochastic evolution equations, SIAM Journal on Mathematical Analysis, (to appear).

Mark Veraar and Lutz Weis, A note on maximal estimates for stochastic convolutions, Czechoslovak Math. J. 61 (2011), no. 3, 743-758.

Jan van Neerven and Lutz Weis, Vector measures of bounded $\gamma$ -variation and stochastic integrals, Vector measures, integration and related topics, Oper. Theory Adv. Appl., vol. 201, Birkhäuser Verlag, Basel, 2010, pp. 303-311.

Christoph Kriegler and Lutz Weis, Contractivity of the $H^\infty$ -calculus and Blaschke products, Operator algebras, operator theory and applications, Oper. Theory Adv. Appl., vol. 195, Birkhäuser Verlag, Basel, 2010, pp. 231-244.

Tuomas P. Hytönen and Lutz Weis, The Banach space-valued BMO, Carleson's condition, and paraproducts, J. Fourier Anal. Appl. 16 (2010), no. 4, 495-513.

Mark Veraar and Lutz Weis, On semi- $\mathcal{R}$ -boundedness and its applications, J. Math. Anal. Appl. 363 (2010), no. 2, 431-443.

Jesus Suarez and Lutz Weis, Addendum to ´Interpolation of Banach spaces by the $\gamma$ -method´, Extracta Math. 24(2009), no. 3, 265-269.

J. M. A. M. van Neerven, M. C. Veraar, and L. Weis, Stochastic evolution equations in UMD Banach spaces, J. Funct. Anal. 255(2008), no. 4, 940-993.

J. M. A. M. van Neerven and L. Weis, Stochastic integration of operator-valued functions with respect to Banach space-valued Brownian motion, Potential Anal. 29 (2008), no. 1, 65-88.

Z. Brzezniak, J. M. A. M. van Neerven, M. C. Veraar, and L. Weis, Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation, J. Differential Equations 245 (2008), no. 1, 30-58.

Cornelia Kaiser and Lutz Weis, Wavelet transform for functions with values in UMD spaces, Studia Math. 186 (2008), no. 2, 101-126.

Nigel Kalton, Jan van Neerven, Mark Veraar, and Lutz Weis, Embedding vector-valued Besov spaces into spaces of $\gamma$ -radonifying operators, Math. Nachr. 281 (2008), no. 2, 238-252.

Tuomas P. Hytönen and Lutz Weis, On the necessity of property $(\alpha)$ for some vector-valued multiplier theorems, Arch. Math.(Basel) 90 (2008), no. 1, 44-52.

Jan van Neerven, Mark Veraar, and Lutz Weis, Conditions for stochastic integrability in UMD Banach spaces, Banach spaces and their applications in analysis, Walter de Gruyter, Berlin, 2007, pp.125-146.

J. M. A. M. van Neerven, M. C. Veraar, and L. Weis, Stochastic integration in UMD Banach spaces, Ann. Probab. 35 (2007), no. 4, 1438-1478.

Zeljko Strkalj and Lutz Weis, On operator-valued Fourier multiplier theorems, Trans. Amer. Math. Soc. 359 (2007), no. 8, 3529-3547.

Tuomas Hytönen and Lutz Weis, Singular convolution integrals with operator-valued kernel, Math. Z. 255 (2007), no. 2, 393-425.

Andreas M. Fröhlich and Lutz Weis, $H^\infty$ calculus and dilations, Bull. Soc. Math. France 134 (2006), no. 4, 487-508.

Jesus Suarez and Lutz Weis, Interpolation of Banach spaces by the $\gamma$ -method, Methods in Banach space theory, London Math. Soc. Lecture Note Ser., vol. 337, Cambridge Univ. Press, Cambridge, 2006, pp. 293-306.

Tuomas Hytönen and Lutz Weis, A $T1$ theorem for integral transformations with operator-valued kernel, J. Reine Angew. Math. 599 (2006), 155-200.#

Nigel Kalton, Peer Kunstmann, and Lutz Weis, Perturbation and interpolation theorems for the $H^\infty$ -calculus with applications to differential operators, Math. Ann. 336 (2006), no. 4, 747-801.

Lutz Weis, The $H^\infty$ holomorphic functional calculus for sectorial operators - a survey, Partial differential equations and functional analysis, Oper. Theory Adv. Appl., vol. 168, Birkhäuser, Basel, 2006, pp. 263- 294.

Johanna Dettweiler, Lutz Weis, and Jan van Neerven, Space-time regularity of solutions of the parabolic stochastic Cauchy problem, Stoch. Anal. Appl. 24 (2006), no. 4, 843-869.

J. M. A. M. van Neerven and L. Weis, Invariant measures for the linear stochastic Cauchy problem and $R$ -boundedness of the resolvent, J. Evol. Equ. 6 (2006), no. 2, 205-228.

Tuomas Hytönen and Lutz Weis, Singular integrals on Besov spaces, Math. Nachr. 279 (2006), no. 5-6, 581-598.

J. M. A. M. van Neerven and L. Weis, Weak limits and integrals of Gaussian covariances in Banach spaces, Probab. Math. Statist. 25 (2005), no. 1, Acta Univ. Wratislav. No. 2784, 55-74.

Markus Duelli and Lutz Weis, Spectral projections, Riesz transforms and $H^\infty$ -calculus for bisectorial operators, Nonlinear elliptic and parabolic problems, Progr. Nonlinear Differential Equations Appl., vol. 64, Birkhäuser, Basel, 2005, pp. 99-111.

Maria Girardi and Lutz Weis, Operator-valued martingale transforms and $R$ -boundedness, Illinois J. Math. 49 (2005), no.2, 487-516 (electronic).

T. Kucherenko and L. Weis, Real interpolation of domains of sectorial operators on $L_p$ -spaces, J. Math. Anal. Appl. 310 (2005), no. 1, 278-285.

J. M. A. M. van Neerven and L. Weis, Stochastic integration of functions with values in a Banach space, Studia Math. 166 (2005), no. 2, 131-170.

Spectral theory in Banach spaces and harmonic analysis, Oberwolfach Rep. 1 (2004), no. 3, 1883-1969, Abstracts from the workshop held July 25-31, 2004, Organized by Nigel Kalton, Alan G. R. McIntosh and Lutz Weis, Oberwolfach Reports. Vol. 1, no. 3.

G. Da Prato, P. C. Kunstmann, I. Lasiecka, A. Lunardi, R. Schnaubelt, and L. Weis, Functional analytic methods for evolution equations, Lecture Notes in Mathematics, vol. 1855, Springer-Verlag, Berlin, 2004, Edited by M. Iannelli, R. Nagel and S. Piazzera.

Maria Girardi and Lutz Weis, Integral operators with operator-valued kernels, J. Math. Anal. Appl. 290 (2004), no. 1, 190-212.

Maria Girardi and Lutz Weis, Criteria for R-boundedness of operator families, Evolution equations, Lecture Notes in Pure and Appl. Math., vol. 234, Dekker, New York, 2003, pp. 203-221.

Maria Girardi and Lutz Weis, Vector-valued extentions of some classical theorems in harmonic analysis, Analysis and applications - ISAAC 2001 (Berlin), Int. Soc. Anal. Appl. Comput., vol. 10, Kluwer Acad. Publ., Dordrecht, 2003, pp. 171-185.

Maria Girardi and Lutz Weis, Operator-valued Fourier multiplier theorems on $L_p(X)$ and geometry of Banach spaces, J. Funct. Anal. 204 (2003), no. 2, 320-354.

Simone Flory, Frank Neubrander, and Lutz Weis, Consistency and stabilization of rational approximation schemes for $C_0$ -semigroups, Evolution equations: applications to physics, industry, life sciences and economics (Levico Terme, 2000), Progr. Nonlinear Differential Equations Appl., vol. 55, Birkhäuser, Basel, 2003, pp. 181-193.

Cornelia Kaiser and Lutz Weis, Perturbation theorems for $\alpha$ -times integrated semigroups, Arch. Math. (Basel) 81 (2003), no. 2, 215-228.

C. Kaiser and L. Weis, A perturbation theorem for operator semigroups in Hilbert spaces, Semigroup Forum 67 (2003), no. 1, 63-75.

Maria Girardi and Lutz Weis, Operator-valued Fourier multiplier theorems on Besov spaces, Math. Nachr. 251 (2003), 34-51.

Allaberen Ashyralyev, Serguei Piskarev, and Lutz Weis, On well-posedness of difference schemes for abstract parabolic equations in $L^p([0,T];E)$ spaces, Numer. Funct. Anal. Optim. 23 (2002), no. 7-8, 669-693.

S. Blunck and L. Weis, Operator theoretic properties of differences of semigroups in terms of their generators, Arch. Math. (Basel) 79 (2002), no. 2, 109-118.

Peer Christian Kunstmann and Lutz Weis, Perturbation theorems for maximal $L_p$ -regularity, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 30 (2001), no. 2, 415-435.

N. J. Kalton and L. Weis, The $H^\infty$ -calculus and sums of closed operators, Math. Ann. 321 (2001), no. 2, 319-345.

S. Blunck and L. Weis, Operator theoretic properties of semigroups in terms of their generators, Studia Math. 146 (2001), no. 1, 35-54.

Lutz Weis, Operator-valued Fourier multiplier theorems and maximal $L_p$ -regularity, Math. Ann. 319 (2001), no. 4, 735-758.

Lutz Weis, A new approach to maximal $L_p$ -regularity, Evolution equations and their applications in physical and life sciences (Bad Herrenalb, 1998), Lecture Notes in Pure and Appl. Math., vol. 215, Dekker, New York, 2001, pp. 195-214.

V. Goersmeyer and L. Weis, Norm continuity of $c_0$ -semigroups, Studia Math. 134 (1999), no. 2, 169-178.

Lutz Weis and Dirk Werner, The Daugavet equation for operators not fixing a copy of $C[0,1]$ , J. Operator Theory 39 (1998), no. 1, 89-98.

Lutz Weis, A short proof for the stability theorem for positive semigroups on $L_p(\mu)$ , Proc. Amer. Math. Soc. 126 (1998), no. 11, 3253-3256.

Lutz Weis, Stability theorems for semi-groups via multiplier theorems, Differential equations, asymptotic analysis, and mathematical physics (Potsdam, 1996), Math. Res., vol. 100, Akademie Verlag, Berlin, 1997, pp. 407-411.

Lutz Weis and Volker Wrobel, Asymptotic behavior of $C_0$ -semigroups in Banach spaces, Proc. Amer. Math. Soc. 124 (1996), no. 12, 3663-3671.

L. Weis, Gaussian estimates and analytic semigroups, Partial differential operators and mathematical physics (Holzhau, 1994), Oper. Theory Adv. Appl., vol. 78, Birkhäuser, Basel, 1995, pp. 397-403.

J. M. A. M. van Neerven, B. Straub, and L. Weis, On the asymptotic behaviour of a semigroup of linear operators, Indag. Math. (N.S.) 6 (1995), no. 4, 453-476.

Lutz Weis, The stability of positive semigroups on $L_p$ spaces, Proc. Amer. Math. Soc. 123 (1995), no. 10, 3089-3094.

E. Teske and L. Weis, Growth and range conditions for the Laplace representation of vector-valued functions, Beiträge zur angewandten Analysis und Informatik, Shaker, Aachen, 1994, pp. 314-334.

L. Weis, Inversion of the vector-valued Laplace transform in $L_p(X)$ -spaces, Differential equations in Banach spaces (Bologna, 1991), Lecture Notes in Pure and Appl. Math., vol. 148, Dekker, New York, 1993, pp. 235-253.

Lutz Weis, Sublattices of $M(X)$ isometric to $M[0,1]$ , Geometry of Banach spaces (Strobl, 1989), London Math. Soc. Lecture Note Ser., vol. 158, Cambridge Univ. Press, Cambridge, 1990, pp. 257-270.

Lutz W. Weis, Banach lattices with the subsequence splitting property, Proc. Amer. Math. Soc. 105 (1989), no. 1, 87-96.

L. W. Weis, A generalization of the Vidav-Jörgens perturbation theorem for semigroups and its application to transport theory, J. Math. Anal. Appl. 129 (1988), no. 1, 6-23.

Lutz W. Weis, A structure theorem for operators on $C(K)$ , Colloquium 1985-86 (Badajoz, 1985-86), Publ. Dep. Mat. Univ. Extremadura, vol. 15, Univ. Extremadura, Badajoz, 1987, pp. 87-96.

Lutz Weis, An extrapolation theorem for the $0$ -spectrum, Aspects of positivity in functional analysis (Tübingen, 1985), North-Holland Math. Stud., vol. 122, North-Holland, Amsterdam, 1986, pp. 261-269.

L. Weis, An alternative proof for the hyper-contractivity of the Ornstein-Uhlenbeck semigroup on the Fock space, Semesterberichte Funktionalanalysis Tübingen 1985/86 (1986), 7-15.

Lutz W. Weis, On the essential order spectrum, Extracta mathematicae 1 (1986), no. 2, 88-90.

Lutz W. Weis, The range of an operator in $C(X)$ and its representing stochastic kernel, Arch. Math. (Basel) 46 (1986), no. 2, 171-178.

Lutz W. Weis, Two examples concerning a theorem of Burgess and Mauldin, Ann. Probab. 13 (1985), no. 3, 1028-1031.

L. W. Weis, On the computation of some quantities in the theory of Fredholm operators, Proceedings of the 12th winter school on abstract analysis (Srni , 1984), no. Suppl. 5, 1984, pp. 109-133.

L. Weis, Approximation by weakly compact operators in $L_1$ , Math. Nachr. 119 (1984), 321-326.

Lutz W. Weis, A characterization of Enflo-operators, Proceedings of the second international conference on operator algebras, ideals, and their applications in theoretical physics (Leipzig, 1983) (Leipzig), Teubner-Texte Math., vol. 67, Teubner, 1984, pp. 220-231.

Lutz W. Weis, Decompositions of positive operators and some of their applications, Functional analysis: surveys and recent results, III (Paderborn, 1983), North-Holland Math. Stud., vol. 90, North-Holland, Amsterdam, 1984, pp. 95-115.

Lutz W. Weis, A characterization of orthogonal transition kernels, Ann. Probab. 12 (1984), no. 4, 1224-1227.

L. Weis, The representation of $L_1$ -operators by stochastic kernels and some operator properties connected with it, Seminaire Choquet-Rogalski-St. Raimond, 23ème, Annee-1983/84, Univ. Pierre Marie Curie, Paris, 1984, pp. 1-7.

L. Weis, On the representation of order continuous operators by random measures, Trans. Amer. Math. Soc. 285 (1984), no. 2, 535-563.

L. Weis, Diffuse stochastische Kerne, Proceedings of the conferences on vector measures and integral representations of operators, and on functional analysis/Banach space geometry (Essen, 1982) (Essen), Vorlesungen Fachbereich Math. Univ. Essen, vol. 10, Univ. Essen, 1983, pp. 213-222.

L. Weis, A note on diffuse random measures, Z. Wahrsch. Verw. Gebiete 65 (1983), no. 2, 239-244.

H. König and L. Weis, On the eigenvalues of orderbounded integral operators, Integral Equations Operator Theory 6 (1983), no. 5, 706-729.

Lutz Weis, Integral operators and changes of density, Indiana Univ. Math. J. 31 (1982), no. 1, 83-96.

Lutz Weis, Perturbation classes of semi-Fredholm operators, Math. Z. 178 (1981), no. 3, 429-442.

Walter Schachermayer and Lutz Weis, Almost compactness and decomposability of integral operators, Proc. Amer. Math. Soc. 81 (1981), no.4, 595-599.

E. Schock and L. Weis, Lineare Integralgleichungen und Funktionalanalysis, Festschrift 10 Jahre Universität Kaiserslautern, 1980, pp. 37-40.

Lutz Weis, Über schwach folgenpräkompakte Operatoren, Arch. Math. (Basel) 30 (1978), no. 4, 411-417.

L. Weis, On perturbations of Fredholm operators in $L_{p}(\mu)$ -spaces, Proc. Amer. Math. Soc. 67 (1977), no. 2, 287-292.

E. Schock and L. Weis, Einige Aspekte der Funktionalanalysis, Jber. Deutsch. Math.-Verein. 77 (1975), 138-159.

Lutz Weis, On the surjective (injective) envelope of strictly (co-) singular operators, Studia Math. 54 (1975), no. 3, 285-290.