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,
*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 L*. Integral Equations Operator Theory^{p}–L^{q}regularity for parabolic partial differential equations on manifolds with cylindrical ends**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 (requires ZMATH access).

The PDF-files on this webpage represent only preliminary versions. Please consult the published articles for work in final form.