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

 

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

 

Book: Functional Calculus of Pseudodifferential Boundary Problems, Progress in Mathematics Volume 65, Second Edition 1996, Birkhδuser, 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.ps   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, AbGrWo11

 

Extension theory for elliptic partial differential operators with pseudodifferential methods. arXiv:1008.1081 To appear in Proceedings of Leiden meeting Dec. 2009, a London Math. Soc. lecture note

 

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 , to appear in Math. Scand.

 

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