Some recent (and a few old) publications and preprints


A characterization of the non-local boundary value problems associated with an elliptic operator, Annali Scuola Normale Superiore  Pisa

22 (1968), 425—513.G68.pdf


Les problems aux limites généraux d’un opérateur elliptique, provenant de la théorie variationnelle, Bull. Sc. Math. 94 (1970), 113—157. BullSci70.pdf


On coerciveness and semiboundedness general boundary problems, Israel J. Math. 10 (1971), 32-95 . G71.pdf


Properties of normal boundary problems for elliptic even-order systems,  Ann. Sc. Norm. Sup. Pisa, Ser. IV, 1 (1974), 1—61.  G74.pdf


(With V. A. Solonnikov) Solution of parabolic pseudo-differential initial-boundary value problems, J. Diff. Eq. 87 (1990), 256-304. GSol90.pdf


Pseudo-differential boundary problems in Lp spaces, Comm. Part. Diff. Eq. 15 (1990), 289-340.  CPDE90.pdf


Book: Functional Calculus of Pseudodifferential Boundary Problems, Progress in Mathematics Volume 65, Second Edition 1996, Birkhäuser, Boston. fun96  (The old files with the full text have been processed recently; pagebreaks differ here and there from the printed book. A few misprints have been corrected.)


(With R. T. Seeley): Zeta and eta functions for Atiyah-Patodi-Singer operators, Journal of Geometric Analysis 6, (1996 ), 31—77 zet96.pdf


(With R. T. Seeley) Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems, Inventiones Math. 121 (1995), 481—529.


Parametrized pseudodifferential  operators and geometric invariants, in  Microlocal Analysis and Spectral Theory (ed L. Rodino),  1997, Kluwer, Dordrecht, pp. 115—164.  param97.pdf


Nonhomogeneous  Navier-Stokes problems in $L_p$ Sobolev spaces over interior and exterior domains, in Theory of the Navier-Stokes Equations, Ser. Adv. Math. Appl. Sci. 47 (eds.J. G. Heywood, K. Masuda, R. Rautmann, V. Solonnikov), World Scientific, Singapore 1998, pp. 46—63. nonhom97.pdf


(With P. B. Gilkey) Logarithmic terms in asymptotic expansions of heat operator traces, Comm. Part. Diff. Eq.  23 (1998), 777—792.  log97.pdf


Trace expansions for pseudodifferential boundary problems for Dirac-type operators and more general systems, Arkiv f. Mat. 37 (1999), 45—86.  G99.pdf  tra97.pdf


Heat trace and resolvent expansions for elliptic systems with pseudodifferential boundary conditions, preprint May 1997. Longer version of the abovementioned Arkiv f. Mat paper.   heat97.pdf


A weakly polyhomogeneous calculus for pseudodifferential boundary problems, J. Functional An. 184 (2001), 19—76. wphg01.pdf


Poles of zeta and eta functions for perturbations of the Atiyah-Patodi-Singer problem, Comm. Math. Phys. 215 (2001) 583—589.  pol00.pdf 


(With E. Schrohe) Trace expansions and the noncommutative residue for manifolds with boundary, J. Reine Angew. Math. 536 (2001), 167—207.  res01.pdf


Nonhomogeneous Dirichlet Navier-Stokes problems in low regularity $L_p$ Sobolev spaces, J. Math. Fluid Mech. 3 (2001) 57—81. dirnav00.pdf 


Trace formulas for parameter-dependent pseudodifferential operators, Nuclear Physics B (Proc. Suppl.) 104 (2002), 71—88. nap02.pdf


(With  L. Hansen) Complex powers of resolvents of pseudodifferential operators, Comm. Part. Diff. Eq. 27 (2002), 2333—2361. powers02.pdf


Logarithmic terms in trace expansions of Atiyah-Patodi-Singer problems, Ann. Global An. Geom. 24 (2003), 1—51.  apslog02.pdf 


Spectral boundary conditions for generalizations of Laplace and Dirac operators, Comm. Math. Phys. 240 (2003), 243—280.  spec02.pdf


A resolvent approach to traces and zeta Laurent expansions, in  AMS Contemp. Math. Proc. 366 ``Spectral Geometry and Manifolds with Boundary and Decomposition of Manifolds''  2005, 67—93.  laur03.pdf


Analysis of invariants associated with spectral boundary problems for elliptic operators, in AMS Contemp. Math. Proc. 366 ``Spectral Geometry and Manifolds with Boundary and Decomposition of Manifolds'' 2005, 43—64. inv04.pdf


(With E. Schrohe) Traces and quasi-traces on the Boutet de Monvel algebra, Ann. Inst. Fourier 54 (2004), 1641—1696. qtra03.pdf


On the logarithm component in trace defect formulas, Comm. Part. Diff. Equ. 30 (2005), 1671—1716.  cpde0418.pdf


Remarks on nonlocal trace expansion coefficients, in ``Analysis, Geometry and Topology of Elliptic Operators,'' (eds. B. Booss-Bavnbek, S. Klimek, M. Lesch, W. Zhang), World Scientific, Singapore 2006, 215—234. koef05.pdf


Known and unknown results on elliptic boundary problems, Bull. Amer. Math. Soc. 43 (2006), 227—230. know05.pdf


Trace defect formulas and zeta values for boundary operators, Proceedings of a workshop at MPI-Bonn 2005: "Traces in Geometry, Number Theory and Quantum Fields" (Sergio Albeverio, Matilde Marcolli, Sylvie Paycha and Jorge Plazas, eds.) Aspects of Mathematics E 38, Vieweg Verlag , 2008, pages 137--153.  bonn06.pdf


(With A. Gaarde) Logarithms and sectorial projections for elliptic boundary problems, Math. Scand. 103 (2008), 243-277, arXiv:math/0703878.


The local and global parts of the basic zeta coefficient for pseudodifferential boundary operators, Math. Ann. 341 (2008), 735—788. arXiv: math.AP/0611854. mathann08.pdf


Book:  Distributions and Operators, Graduate Text in Mathematics 252, Springer-Verlag, New York 2009, 461 pp. Corrections corrections , additional exercises miscellaneous .


(With B.M. Brown and I. G. Wood)  M-functions for closed extensions of adjoint pairs of operators, with applications to elliptic boundary problems,  Math. Nachr. 282 (2009), 314-347. mathnach.pdf


Krein resolvent formulas for elliptic boundary problems in nonsmooth domains, Rend. Sem. Mat. Univ. Pol. Torino 66 (2008), 13-39. arXiv:0810.2741 torino08.pdf


Perturbation of essential spectra of exterior elliptic problems, Applicable Analysis 90 (2011), 103-123,   PertEss11.


Krein-like extensions and the lower boundedness problem for elliptic operators on exterior domains.  arXiv:1002.4549  J. Diff. Eq. 252 (2012), 852-885.


(With H. Abels and I. G. Wood)  Extension theory and Krein-type resolvent formulas for nonsmooth boundary value problems. arXiv:1008.3281,  J. Functional Analysis, 266 (2014), 4037-4100.   JFA14.pdf


Extension theory for elliptic partial differential operators with pseudodifferential methods. arXiv:1008.1081 Operator Methods for Boundary Value Problems, eds. S. Hassi, H. S. V. de Snoo, F. H. Szafraniec, London Math. Soc. Lecture Note Series 404 (2012), 221-258. LMS12.pdf


Spectral asymptotics for Robin problems with a discontinuous coefficient. arXiv:1009.0997 , J. Spectral Theory 1 (2011), 155-177. JST11.pdf


The sectorial projection defined from logarithms. arXiv:1102.4051 , Math. Scand. 111 (2012), 118-126.


The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates.  J. Math. Anal. Appl. 382 (2011) 339–363,  JMAA11.pdf


Spectral asymptotics for nonsmooth singular Green operators, arXiv:1205.0094.  Comm. Part. Diff. Eq. 39:3 (2014), 530-573. CPDE14.pdf


(With H. Gimperlein) Heat kernel estimates for pseudodifferential operators, fractional Laplacians and Dirichlet-to-Neumann operators. J. Evolution Eq. 14 (2014), 49-83. JEE14.pdf


Fractional Laplacians on domains, a development of Hörmander's theory of $\mu$-transmission pseudodifferential operators, arXiv:1310.0951 , Adv. Math. 268 (2015), 478–528


TeX-typed version of  L. Hörmander: Seminar notes on pseudo-differential operators and boundary problems, I.A.S. Princeton 1965-66 LH65.pdf


Local and nonlocal boundary conditions for $\mu$-transmission and fractional elliptic pseudodifferential operators,  Analysis and PDE  7 No. 7 (2014), 1649-1682. APDE14.pdf


(With Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik)  Spectral asymptotics for resolvent differences of elliptic operators with $δ$ and $δ^\prime$-interactions on hypersurfaces, J. Spectral Theory  5 (2015), No. 4, 697–729. JST15.pdf


Spectral results for mixed problems and fractional elliptic operators, arXiv:1407.0932,  J. Math. Anal. Appl. 421 (2015), 1616-1634. JMAA15.pdf


Regularity of spectral fractional Dirichlet and Neumann problems, arXiv:1412.3744 , Math. Nachr. 289 (2016), 831-844. MN16.pdf


Integration by parts and Pohozaev identities for space-dependent fractional-order operators. arXiv:1511.02109, J. Differential Equations 261 No. 3, 1835-1879. JDE16.pdf


Green's formula and a Dirichlet-to-Neumann operator for fractional-order pseudodifferential operators, Comm. Part. Diff. Eq. 43 No. 5 (2018), 750-789. arXiv:1611.03024


Regularity in Lp Sobolev spaces of solutions to fractional heat equations. J. Functional Analysis (2018). JFA18.pdf


Fractional-order operators: boundary problems, heat equations. In “Mathematical Analysis and Applications – Plenary Lectures, Isaac 2017 Vaxjo Sweden”, Springer Proceedings in Mathematics and Statistics, Springer, Switzerland 2018, pp. 51-81.  arXiv:1712.01196


Limited regularity of solutions to fractional heat and Schrödinger equations, to appear in Discr. Cont. Dyn. Syst. A, 39 No. 6 (2019). arXiv:1806.10021