Papers by Richard Melrose, often with coauthors

• Generalized backscattering and the Lax-Phillips transform

  with Gunther Uhlmann
  Arxiv: math.AP/0712.4236
  Initial version of 27 December, 2007.
  Small corrections, 2 January December, 2008.
  Further small corrections, 3 January December, 2008.
  (But really a chapter from an old book manuscript!)
  BackScat.dvi
  BackScat.ps (postscript file)
  BackScat.pdf (acrobat file)
  

• Propagation of singularities for the wave equation on edge manifolds

  with András Vasy and Jared Wunsch
  Arxiv: math.AP/0612750
  Initial version of 24 December, 2006.
  New version, 5th November, 2007:
  Edges.dvi
  Edges.ps (postscript file)
  Edges.pdf (acrobat file)
  

• Equivariant and fractional index of projective elliptic operators

  with Varghese Mathai and Is Singer
  Arxiv: math.DG/0611819
  Initial version of 27 November, 2006.
  New version, 11 May, 2007:
  JDG version, 28 March, 2008:
  Fract-equiv-index.dvi
  Fract-equiv-index.ps (postscript file)
  Fract-equiv-index.pdf or JDG version (acrobat file)
  

• Periodicity and the determinant bundle

  with Frédéric Rochon
  Revised version of 29 November, 2006.
  Initial version of 15 June, 2006.
  perdet.dvi
  perdet.ps (postscript file)
  perdet.pdf (acrobat file)
  

• Index in K-theory for Families of fibred cusp operators
  

  with Frédéric Rochon
  Initial version of 4 July, 2005.
  New version (on Arxiv as 0507590)
  Revised version of 4 March 2006 (to appear in K Theory).
  faficu.dvi
  faficu.ps (postscript file)
  faficu.pdf (acrobat file)
  

• Star products and local line bundles
  

  Initial version of 11 July, 2004.
  Current version, 5 October, 2004. Accepted for publication in l'Annales de l'Institut Fourier, special volume for Louis Boutet de Monvel
  spallb.dvi
  spallb.ps (postscript file)
  spallb.pdf (acrobat file)
  

• Fractional analytic index
  

  with V. Mathai and I.M. Singer
  Version of 20 Feb, 2004 -- essentially as on Arxiv:DG/0402329; relation to Cheeger-Simons added.
  [Version of 17 Feb, 2004].
  Originally posted 3 Feb, 2004
  mms3.dvi
  mms3.ps (postscript file)
  mms3.pdf (acrobat file)
  

• The inverse spectral problem for planar domains
  

  Lectures at ANU that I had forgotten to put on the web!
  anulec.dvi (You will need these twelve eps files too if you want the figures)
  
  • anulec1.eps)
    
  • anulec2.eps)
    
  • anulec3.eps)
    
  • anulec4.eps)
    
  • anulec5.eps)
    
  • anulec6.eps)
    
  • anulec7.eps)
    
  • anulec8.eps)
    
  • anulec9.eps)
    
  • anulec10.eps)
    
  • anulec11.eps)
    
  • anulec12.eps)
    
  anulec.ps (postscript file)
  anulec.pdf (acrobat file)
  

• Families index for pseudodifferential operators on manifolds with boundary
  

  with Frédéric Rochon
  Version of 25 May, 2003
  fipomb.dvi
  fipomb.ps (postscript file)
  fipomb.pdf (acrobat file)
  

• The index of projective families of elliptic operators
  

  with V. Mathai and I.M. Singer
  Originally posted 31 May, 2002; Version of 1 June, 2002
  mms2001.dvi
  mms2001.ps (postscript file)
  mms2001.pdf (acrobat file)
  

• Propagation of singularities for the wave equation on conic manifolds
  

  with Jared Wunsch
  Version of 22 November (original 29 October), 2001
  melwun1.dvi
  melwun1.ps (postscript file)
  melwun1.pdf (acrobat file)
  

• Spectral and scattering theory for symbolic potentials of order zero, I
  

  with Andrew Hassell and András Vasy
  Version of 13 December, 2001
  HMV1.dvi
  HMV1.ps (postscript file)
  HMV1.pdf (acrobat file)
  

• A remark on distributions and the de Rham theorem
  

  If you have seen this sort of proof somewhere, please let me know! Original posted November 17, 1999
  Version of January 22, 2000: Some typos corrected (thanks to Jukka Liukkonen)

  deRham.dvi
  deRham.ps (postscript file)
  deRham.pdf (acrobat file)
  

• Contact degree and the index of Fourier integral operators
  Joint work with C. Epstein

  To appear in Mathematics Research Letters
  Version from proofs, May 27, 1998
  

  (First version 2nd February 1998)
  cdifio.dvi
  cdifio.ps (postscript file)
  cdifio.pdf (acrobat file)
  

• Contact degree
  Superceded by the paper above. Joint work with C. Epstein

  This is a short note describing an extended form of Weinstein's question on the index of Fourier integral operators in terms of the notion of the `degree' of a contact diffeomorphism
  Version of January 8, 1998.
  (postscript file)
  ConDeg.pdf (acrobat file)

• Pseudodifferential operators on manifolds with fibred boundaries
  Joint work with Rafe Mazzeo

  To appear in the special volume of the Asian Journal of Mathematics celebrating the 70th birthday of Professor Mikio Sato.
  Version of 10th of March, 1999 (another typo squashed).
  poomwfb.dvi
  (dvi)
  double.eps
  (figure)
  Triple.eps(figure)
  poomwfb.ps
  (postscript)
  poomwfb.pdf
  (acrobat)
  

• Homology and the Heisenberg algebra
  Joint work with C. Epstein and G. Mendoza

  (not the Eisenberg algebra as originally advertised!)
  

  Short write up for a seminar at Ecole Poytechnique, may 20, 1997
  

  Version of July 7, 1997.
  HoHe.dvi (amslatex dvi file with encapsulated postscript inserts)
  HoHe.ps (postscript file)

• Geometric optics and the bottom of the spectrum

  Written up (and extended) version of a talk at the meeting
  `Geometrical optics and related topics'
  at Cortona, September 1996.

  Version of November 8, 1996.
  Abstract
  Cortona.dvi (amstex dvi file)
  Cortona.ps (postscript file)

• K-theory of $C^*$-algebras of b-pseudodifferential operators

  (Old title: K-theory of b-pseudodifferential operators and an {$\RR^k$}-equivariant index theorem)
  

  with Victor Nistor

  Preprint, October 18, 1996.
  Abstract
  (Revised version of September 10, 1997)
  ktobpo.ps (In postscript format)
  ktobpo.pdf (In acrobat format)
  ktobpo.dvi (In dvi format)
  

• Homology of pseudodifferential operators I.
  Manifolds with boundary

  with Victor Nistor

  Preprint, May 29, 1996.
  Abstract
  hopo1.ps (postscript file)

• Fibrations, compactifications and
  algebras of pseudodifferential operators

  Published in: ``Partial Differential Equations and Mathematical Physics. The Danish-Swedish Analysis Seminar, 1995''
  Editors, Lars H\"ormander and Anders Melin.
  Birkhauser, 1996.
  Pages 246-261.
  Abstract
  fcaaopo.ps (postscript file)

• The eta invariant of pseudodifferential operators

  Published in: Math. Res. Letters, Vol 2, No. 5, 1995, pp 541-561
  Abstract
  teiafp.ps (postscript file)

• Scattering metrics and geodesic flow at infinity

  with Maciej Zworski

  Published in: Invent. Math., Vol 124 (1996), pp 389-436.
  Abstract
  [Diagrams are currently missing from smagai]
  smagai.ps (postscript file)
  smagai.pdf (acrobat file)

• Signature theorem for manifolds with corners
  of codimension 2

  with Andrew Hassell and Rafe Mazzeo

  To appear in Topology
  (revised September 10, 1996)
  Abstract
  stmwc.ps (postscript file)
  stmwc.pdf (Adobe portable document format file)

• Spectral and scattering theory for the Laplacian
  on asymptotically Euclidian spaces

  Published in: "Spectral and scattering theory",
  Edited by M. Ikawa, 1994, Marcel Dekker.
  Introduction
  As published: sslaes.ps (postscript file)

  Corrected , (Jan 15, 1997):
  sslaes1.dvi (dvi file, needs lamstex fonts)
  sslaes1.ps (postscript file)

  sslaes1.pdf (acrobat file)

• An index theorem for families of Dirac operators
  on odd-dimensional manifolds with boundary

  with Paolo Piazza

  J. Diff. Geom. 46 (1997) 287-334
  Abstract
  ofapsi.ps (postscript file)

• Families of Dirac operators, boundaries
  and the b-calculus

  with Paolo Piazza

  J. Diff. Geom. 46 (1997) 99-180
  Abstract
  fdobbc.ps (postscript file)

• Semi-linear Diffraction of Conormal Waves

  with Antonio Sa Barreto and Maciej Zworski

  Asterisque. sldall.ps
  

• Pseudodifferential operators, corners and singular limits

  talk at ICM in Kyoto, 1990

  kyoto.dvi
  kyoto.ps (postscript)
  kyoto.pdf (acrobat)
  

• Isospectral sets of drumheads are compact in C^∞

  Unpublished preprint from MSRI, 048-83, 1983

  isospectral.pdf (acrobat file)
  isospectral.dvi(dvi file)
  isosp.pdf (acrobat -- scan of the preprint)
  

• Elliptic operators of totally characteristic type

  with Gerardo Mendoza: Unpublished preprint from MSRI, 047-83, 1983

  b-elliptic-1983.pdf (acrobat file -- needs proofreading!)
  b-elliptic-1983.dvi(dvi file -- needs proofreading!)
  1983-Melrose-Mendoza.pdf (acrobat -- scan of the preprint)