Global Analysis and Partial Differential Equations, in particular PDEs on singular and noncompact manifolds. This includes:
Regularity and Asymptotics of Solutions
Boundary Value Problems
Spectral Theory
Operator Algebras
T. Krainer, A Shubin pseudodifferential calculus on asymptotically conic manifolds. J. Fourier Anal. Appl. 31 (2025), Article 44. PDF-file.
T. Krainer, Cobordism invariance of the index for realizations of elliptic operators revisited. To appear in Rocky Mt. J. Math. PDF-file.
T. Krainer, Extensions of symmetric operators that are invariant under scaling and applications to indicial operators. New York J. Math. 28 (2022), 705–772. PDF-file.
T. Krainer and G. Mendoza, Elliptic complexes of first-order cone operators: ideal boundary conditions. Math. Nachr. 291 (2018), 1815–1850. PDF-file.
T. Krainer and G. Mendoza, The Friedrichs extension for elliptic wedge operators of second order. Adv. Differential Equations 23 (2018), 295–328. PDF-file.
T. Krainer and G. Mendoza, Boundary value problems for first order elliptic wedge operators. Amer. J. Math. 138 (2016), 585–656. PDF-file.
T. Krainer and G. Mendoza, Boundary value problems for elliptic wedge operators: the first order case. In: J. Escher, E. Schrohe, J. Seiler, and C. Walker (Eds.), Elliptic and Parabolic Equations, pp. 209–232. Springer Proceedings in Mathematics & Statistics, Vol. 119, 2015. PDF-file.
T. Krainer, A calculus of abstract edge pseudodifferential operators of type ρ,δ. In: J. Escher, E. Schrohe, J. Seiler, and C. Walker (Eds.), Elliptic and Parabolic Equations, pp. 179–207. Springer Proceedings in Mathematics & Statistics, Vol. 119, 2015. PDF-file.
T. Krainer and G. Mendoza, Elliptic systems of variable order. Rev. Mat. Iberoam. 31 (2015), 127–160. PDF-file.
T. Krainer and G. Mendoza, The kernel bundle of a holomorphic Fredholm family. Comm. Partial Differential Equations 38 (2013), 2107–2125. PDF-file.
J. Gil, T. Krainer, and G. Mendoza, On the closure of elliptic wedge operators. J. Geom. Anal. 23 (2013), 2035–2062. PDF-file.
J. Gil, T. Krainer, and G. Mendoza, Dynamics on Grassmannians and resolvents of cone operators. Anal. PDE 4 (2011), 115–148. PDF-file.
T. Krainer, On the completeness of the generalized eigenfunctions of elliptic operators on manifolds with conical singularities. Math. Nachr. 283 (2010), 1680–1695. PDF-file.
J. Gil, T. Krainer, and G. Mendoza, Trace expansions for elliptic cone operators with stationary domains. Trans. Amer. Math. Soc. 362 (2010), 6495–6522. PDF-file.
T. Krainer, On the expansion of the resolvent for elliptic boundary contact problems. Ann. Global Anal. Geom. 35 (2009), 345–361. PDF-file.
T. Krainer, Maximal Lp–Lq regularity for parabolic partial differential equations on manifolds with cylindrical ends. Integral Equations Operator Theory 63 (2009), 521–531. PDF-file.
J. Gil, T. Krainer, and G. Mendoza, A conic manifold perspective of elliptic operators on graphs. J. Math. Anal. Appl. 340 (2008), 1296–1311. PDF-file.
R. Denk and T. Krainer, R-boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators. Manuscripta Math. 124 (2007), 319–342. PDF-file.
J. Gil, T. Krainer, and G. Mendoza, On rays of minimal growth for elliptic cone operators. Oper. Theory Adv. Appl. 172 (2007), 33–50. PDF-file.
T. Krainer, Elliptic boundary problems on manifolds with polycylindrical ends. J. Funct. Anal. 244 (2007), 351–386. PDF-file.
T. Krainer, Resolvents of elliptic boundary problems on conic manifolds. Comm. Partial Differential Equations 32 (2007), 257–315. PDF-file.
J. Gil, T. Krainer, and G. Mendoza, Geometry and spectra of closed extensions of elliptic cone operators. Canad. J. Math. 59 (2007), 742–794. PDF-file.
J. Gil, T. Krainer, and G. Mendoza, Resolvents of elliptic cone operators. J. Funct. Anal. 241 (2006), 1–55. PDF-file.
T. Krainer and B.-W. Schulze, Long-time asymptotics with geometric singularities in the spatial variables. Contemp. Mathematics 364 (2004), 103–126. PDF-file.
T. Krainer, On the inverse of parabolic boundary value problems for large times. Japanese J. Math. 30 (2004), 91–163. PDF-file.
T. Krainer and B.-W. Schulze, The conormal symbolic structure of corner boundary value problems. Oper. Theory Adv. Appl. 155 (2004), 19–64. PDF-file.
T. Krainer and B.-W. Schulze, On the inverse of parabolic systems of partial differential equations of general form in an infinite space-time cylinder. Oper. Theory Adv. Appl. 138 (2002), 93–278. PDF-file.
T. Krainer, The calculus of Volterra Mellin pseudodifferential operators with operator-valued symbols. Oper. Theory Adv. Appl. 138 (2002), 47–91. PDF-file.
T. Krainer, Volterra families of pseudodifferential operators. Oper. Theory Adv. Appl. 138 (2002), 1–45. PDF-file.
J. Gil (with T. Krainer and G. Mendoza), On the closure of elliptic wedge operators. In: D. Grieser, S. Teufel, and A. Vasy (Eds.), Microlocal Methods in Mathematical Physics and Global Analysis, pp. 55–58, Trends in Mathematics, Research Perspectives, Birkhäuser, Basel, 2013.
T. Krainer (with J. Gil and G. Mendoza), Trace expansions for elliptic cone operators. In: D. Grieser, S. Teufel, and A. Vasy (Eds.), Microlocal Methods in Mathematical Physics and Global Analysis, pp. 63–67, Trends in Mathematics, Research Perspectives, Birkhäuser, Basel, 2013.
J. Gil, T. Krainer, and I. Witt (Eds.), Aspects of Boundary Problems in Analysis and Geometry. Birkhäuser Verlag, Basel, 2004. Link to the Publisher.
Reviews for Mathematical Reviews (requires MathSciNet access).
Reviews for Zentralblatt MATH.
The PDF-files on this webpage represent only preliminary versions. Please consult the published articles for work in final form.