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.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,
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