Matthias Lesch

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Publications

I publish my preprints also on the ArXiv e-Print archive.

This list is reasonably complete for the last 10 years or so.

• With Boris Vertman: Regular-singular Sturm-Liouville operators and their zeta-determinants
• With Henri Moscovici and Markus Pflaum: Connes-Chern character for manifolds with boundary and eta cochains, based on svn rev 246.
  Talk at the Noncommutative Geometry conference in Oberwolfach, September 2009: The relative Connes-Chern character for manifolds with boundary.
  Extended abstract ; Slides
  A version of this talk was also delivered at the PIMS (Victoria, BC) in July.
• Pseudodifferential operators and regularized traces.
  Accepted for publication in the Proceedings of the Conference on Motives, Quantum Field Theory and Pseudodifferential Operators, Boston, June 2008, Clay Mathematics Proceedings.
• With Bernhelm Booß-Bavnbek: The invertible double of elliptic operators 25 pages, final version, Dec 30, 2008.
  Lett. Math. Phys. 87 (2009), No 1-2, 19-46
  DOI 10.1007/s11005-009-0292-9
• With Bernhelm Booß-Bavnbek and Chaofeng Zhu: The Calderon Projection: New Definition and Applications , 57 pages, 4 figures
  Journal of Geometry and Physics 59 (2009), No. 7, 784-826
  DOI 10.1016/j.geomphys.2009.03.012 .

  • The invertible double construction for general first order elliptic differential operators. Extended abstract of a talk given on this paper at the Oberwolfach meeting "Analysis and geometric singularities", August 2007.

• With Bernhelm Booß-Bavnbek and Giampiero Esposito: Quantum gravity: unification of principles and interactions, and promises of spectral geometry. Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA 3 (2007) (Symmetry, Integrability and Geometry: Methods and Applications)

• With Henri Moscovici (Columbus) and Markus Pflaum (Frankfurt): Regularized traces and $K$-theory invariants of parametric pseudodifferential operators. Final Revision 2.4 as of March, 2007, US Letter size PDF 19p, ISO a4paper size PDF 17p. In: "Traces in Geometry, Number Theory and Quantum Fields" Sergio Albeverio, Matilde Marcolli, Sylvie Paycha, Jorge Plazas (Editors) Aspects of Mathematics E 38, Vieweg Verlag 2008, pp. 161-177.

• With Henri Moscovici (Columbus) and Markus Pflaum (Frankfurt): Relative pairing in cyclic cohomology and divisor flows. Revision 5.22 as of December 22, 2006: revised and expanded by a factor of 1.5, 43p. Journal of K-theory 3 (2009), No. 2, 359-407,
  10.1017/is008001021jkt051| PDF | ArXiv math.KT/0603500

  Extended abstract of talk delivered at the Oberwolfach--miniworkshop: Zeta Functions, Index and Twisted K-Theory; Interactions with Physics, May 2006 (somewhat outdated)

• Selected aspects of the mathematical work of Krzysztof P. Wojciechowski 16 pages PDF | ArXiv math.SP/0603502.
  In: B. Booss--Bavnbek, Slawomir Klimek, Matthias Lesch, Weiping Zhang (eds.) Analysis, Geometry and Topology of Elliptic Operators - Papers in Honour of Krzysztof P. Wojciechowski's 50th birthday, World Scientific Singapore, 2006, pp. 3-22.

• The uniqueness of the spectral flow on spaces of unbounded self--adjoint Fredholm operators. 32 pages, 2 figures, math.FA/0401411 In: Spectral geometry of manifolds with boundary and decomposition of manifolds (B.~Booss-Bavnbek, G.~Grubb, and K.P. Wojciechowski, eds.), Cont. Math., vol. 366, Amer. Math. Soc., 2005, pp.~193--224.

• With B. Himpel and P. Kirk: Calderon projector for the Hessian of the perturbed Chern-Simons function on a 3-manifold with boundary. Proc. London Math. Soc. 89 (2004), 241--272; math.GT/0302234

• with Paul Kirk: On the Rho invariant for manifolds with boundary. Algebraic and Geometric Topology 3 (2003), 623-675. 34 pages, LaTeX2e, 12 diagrams, download here: math.DG/0203097

• with Bernhelm Booss-Bavnbek and John Phillips: Spectral Flow of Paths of Self-Adjoint Fredholm Operators. In: Quantum Gravity and Spectral Geometry, Naples July 2001 (G. Esposito, G. Miele, B. Preziosi eds.), Nuclear Physics B Proceedings Supplement 104 (2002), 177-180. DVI, PDF

• with Bernhelm Booss-Bavnbek and John Phillips: Unbounded Fredholm Operators and Spectral Flow. Canad. J. Math. 57 (2005), 225--250; 2 figures, revised version of 2004-Feb-12, math.FA/0108014

• with Paul Kirk: The eta-invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary. Forum Math. 16 (2004), 553--629; math.DG/0012123

• with Mark Malamud: On the number of square integrable solutions and self—adjointness of symmetric first order systems of differential equations. J. Diff. Equ. 189 (2003), 556-615. 50 pages, LaTeX2e, math.FA/0012080, DVI, Postscript

• A remark on papers by Shubin on classical and quantum completeness. 8 pages, LaTeX2e math.SP/0005011, DVI,  Postscript

  superceded by

  Essential self-adjointness for symmetric linear relations associated to first order systems.
  18 p., LaTeX2e, In: Seminaire: Equations aux Derivees Partielles. CNRS, Ecole Polytech. (2000), Exp. No. X. math.SP/0005011 (v1), DVI, Postscript

• with Jochen Brüning: On boundary value problems for Dirac type operators. I. Regularity and self-adjointness. J. Funct. Anal. 185 (2001), 1--62; 55 pages, LaTeX2e. math.FA/9905181, DVI, Postscript

• with Daniel Grieser: On the L^2-Stokes theorem and Hodge theory for singular algebraic varieties.16 pages, LaTeX2e. math.DG/9902062, Math. Nachr. 246-247 (2002), 68-82; SRC, DVI, Postscript

• with Jochen Brüning: Spectral theory of boundary value problems for Dirac type operators. Geometric aspects of partial differential equations (Roskilde, 1998), 203--215, Contemp. Math., 242, Amer. Math. Soc., Providence, RI, 1999. math.DG/9902100, DVI, Postscript

• with Markus Pflaum: Traces on algebras of parameter dependent pseudodifferential operators and the eta-invariant.Trans. Amer. Math. Soc. 352 (2000), no. 11, 4911--4936. Revised version of October 21, 1998. math.FA/9804136, Source, DVI, PS

• with Mark Malamud: The inverse spectral problem for first order systems on the half line.In: Differential operators and related topics, Vol. I (Odessa, 1997), 199--238, Oper. Theory Adv. Appl., 117, Birkhäuser, Basel, 2000. Updated Version of August 28, 1998. math.SP/9805033, Source,  DVI,  PS

• with Jürgen Tolksdorf: On the determinant of one-dimensional elliptic boundary value problems.Commun. Math. Phys. 193 (1998), 643-660. 18 pages, LaTeX2e. Revised version, 12-18-1997. dg-ga/9707022, DVI,  PS

• On the noncommutative residue for pseudodifferential operators with log-polyhomogeneous symbols. Ann. Glob. Anal. Geom. 17 (1999), 151-187. Version of September 15, 1997 dg-ga/9708010, Source, DVI, PS

• with J. Brüning: On the eta-invariant of certain nonlocal boundary value problems.Duke Math. J. 96 (1999), no. 2, 425--468. Revised version, 11-15-1997. dg-ga/9609001, Source, DVI, PS

• with N. Peyerimhoff: An index theorem for manifolds with metric horns.Commun. Part. Diff. Equ. 23 (1998), 649-684. Revised version, 01-20-1998. dg-ga/9609009, Source, DVI,  PS

• Determinants of regular singular Sturm-Liouville operators. Math. Nachr. 194 (1998), 139-170. Revised version, January, 1996. math.DG/9902114, Source,  DVI, PS

• Operators of Fuchs type, conical singularities, and asymptotic methods. Teubner Texte zur Mathematik Vol. 136, Teubner--Verlag, Leipzig, 1997. The book has been out of print for a while since Teubner Verlag has disappeared. The arXiv:dg-ga/9607005 version is identical with the published book version.

• With K. P. Wojciechowski:
  On the eta-invariant of generalized Atiyah-Patodi-Singer boundary value problems. Illinois Journal of Mathematics, 40 (1996), 30-46.
  Article at Project Euclid (Open Access)

• With J. Brüning:
  Kähler-Hodge theory for conformal complex cones. Geom. Funct. Anal. 3 (1993), no. 5, 439-473.
  DOI 10.1007/BF01896238

• With J. Brüning:
  Hilbert complexes. J. Funct. Anal. 108 (1992), no. 1, 88-132.
  DOI 10.1016/0022-1236(92)90147-B

• On the index of the infinitesimal generator of a flow. J. Oper. Theory 25 (1991), 73-92

• The published version of my PhD thesis written under the supervision of Manfred Breuer in Marburg.
  K-theory of Toeplitz C*-algebras on Lie spheres Int. Equ. Oper. Theory 14 (1991), 120-145
  DOI 10.1007/BF01194930