Publications and Preprints

It would be my pleasure to send you a reprint of my articles, just email me, or email if you have any questions or inquires. Also, please email me if you have comments (good or bad) about my articles, especially letting me know of any inaccurate statements, histories, references, errors, ... I will be super grateful! (I try my best to state things accurately, but being human I regretfully fail sometimes.)

Thesis:

  1. Thesis: On the $b$-pseudodifferential calculus on manifolds with corners. gzipped ps file. 78 pages, 1998.

Published Articles:

  1. The Structure of the Resolvent of Elliptic Pseudodifferential Operators. ps file, gzipped ps file. J. Funct. Anal. 184 (2001), no. 1, 77-135.
  2. Tempered Operators and the Heat Kernel and Complex Powers of Elliptic Pseudodifferential Operators. ps file, gzipped ps file. Comm. Partial Differential Equations 26 (2001), no. 7 & 8, 1253-1321.
  3. On the Noncommutative Residue and the Heat Trace Expansion on Conic Manifolds. pdf file. Manuscripta Math. 109 (2002) 3, 309-327. © Springer-Verlag. Joint work with Juan Gil.
  4. On the Resolvent of Differential Operators on Conic Manifolds. ps file, gzipped ps file. Comm. Anal. Geom. 10 (2002), no. 5, 877-934.
  5. Parameter-Dependent Operators and Resolvent Expansions on Conic Manifolds. ps file. Illinois J. Math. 46 (2002), no. 4, 1035-1059.© Univ. of Illinois.
  6. Regularity of Solutions of the Heat Equation on a Cone. ps file. Int. Math. Res. Not. 3 (2003), 161-178. Joint work with Thalia Jeffres.
  7. Complex Powers of Differential Operators on Manifolds with Conical Singularities. ps file. J. Anal. Math. 89 (2003), 31-56.
  8. Asymptotic Properties of the Heat Kernel on Conic Manifolds. ps file. Israel J. Math. 136 (2003), 285-306.
  9. Index theory of Dirac Operators on Manifolds with Corners up to Codimension Two. pdf file. Aspects of Boundary Problems in Analysis and Geometry, Birkhauser, Boston, 131-169, 2004.
  10. Regularity of the Heat Operator on a Manifold with Cylindrical Ends. pdf file. Joint work with Thalia Jeffres. Pacific J. Math. 215 (2004) no. 2, 331-345. © Pacific J. Math.
  11. The $\z$-determinant of generalized APS boundary problems over the cylinder. pdf file. Joint work with Jinsung Park. J. Phys. A: Math. Gen. 37 (2004), issue 29, pages 7381 - 7392.
  12. Decomposition of the zeta-determinant for the Laplacian on manifolds with cylindrical end. pdf file. Joint work with Jinsung Park. Illinois J. Math. 48 (2004), no. 4, 1279--1303. © Univ. of Illinois. Gluing formula for the zeta-determinant of Laplace type operators --- does not apply to Dirac operators (with global BVP), which is the focus of the Advances paper below.
  13. On gluing formulae for the spectral invariants of Dirac type operators. pdf file. (This is a survey/announcement paper only ... no proofs! ) Joint work with Jinsung Park. Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 1--11.
  14. Dirac operators, Boundary Value Problems, and the b-Calculus. pdf file. AMS Contemporary Math. Proceedings volume on Spectral Geometry of Manifolds with Boundary, edited by B. Booss-Bavnbek, G. Grubb and K. P. Wojciechowski, 2005.
  15. The Index of $b$-pseudodifferential Operators on Manifolds with Corners. pdf file.
    16. Ann. Global Anal. Geom. 27 (2005), no. 2, 101--133.
  16. Functional determinants for the Dirac equation with mixed pseudodifferential boundary conditions over finite cylinders. pdf file. Joint work with Jinsung Park. J. Math. Phys. 46 (2005), no. 4, 042309, 13 pp.
  17. On the gluing problem for Dirac operators on manifolds with cylindrical ends. pdf file. Joint work with Jinsung Park. J. Geom. Anal. 15 (2005), no. 2, 285--319.
  18. $\z$-determinants of Laplacians with Neumann and Dirichlet boundary conditions. pdf file. Joint work with Jinsung Park. J. Phys. A: Math. Gen. 38 (2005) 8967-8977.
  19. Relative formulae for the spectral invariants of the b-calculus and generalized APS boundary problems of Dirac operators. pdf file. Joint work with Jinsung Park. Pacific J. Math. 223 (2006), no. 2, 317--331.
  20. The very unusual properties of the resolvent, heat kernel, and zeta function for the operator -d^2/dr^2 - 1/(4r^2). pdf file. J. Math. Phys. 47 (2006), no. 4, 043506, 27 pp.
  21. On the gluing problem for the spectral invariants of Dirac operators. pdf file. Joint work with Jinsung Park. Adv. in Math. 202 (2006), no. 2, 401--450.
  22. Residue Traces and Kernel Expansions of Pseudodifferential Operators. ps file. Modern trends in geometry and topology, 251--264, Cluj Univ.\ Press, Cluj-Napoca, 2006.
  23. Boundary problems for Dirac type operators on manifolds with multi-cylindrical end boundaries. pdf file. Joint work with Jinsung Park. Ann. Global Anal. Geom. 29 (2006), no. 2, 103--144.
  24. Zeta functions of Dirac and Laplace-type operators over finite cylinders. pdf file. Joint work with Jinsung Park and Klaus Kirsten. Ann. Physics 321 (2006), no. 8, 1814--1842.
  25. Zeta Regularized Determinants for Conic Manifolds. pdf file. J. Funct. Anal., 242 (2007), no. 1, 195--229.
  26. Geometric BVPs, Hardy spaces, and the Cauchy integral and transform on regions with corners. pdf file. J. Differential Equations, 239 (2007), 132-–195.

Preprints:


    Spectral invariants of Dirac operators:
  1. Adiabatic limit of the Eta invariant over cofinite quotient of $\mathrm{PSL}(2,\R)$. pdf file. Joint work with Sergiu Moroianu and Jinsung Park.

    2. Other preprints:
  2. Resolvents of cone pseudodifferential operators, asymptotic expansions and applications. pdf file. Joint work with Juan Gil.
  3. Fredholm Perturbations of Dirac Operators on Manifolds with Corners. pdf file. Joint work with Richard Melrose.

 
 

Last Modified: 4-5-06