Roger Nichols, Ph.D.

         Contact Information:

              Mathematics Department
              The University of Tennessee at Chattanooga
              415 EMCS Building, Dept. 6956
              615 McCallie Ave
              Chattanooga, TN 37403, USA

 

              E-mail:  roger-nichols "at" utc.edu

              Office:   EMCS 418A
              Phone:  (423) 425-4036
              Fax:       (423) 425-4586

 

 About Me:

I am an associate professor in the Department of Mathematics at The University of Tennessee at Chattanooga.


 Research Interests:

Spectral theory of differential operators, functional analysis, and approximation theory.


 Publications:

2011

  • Spectral properties of discrete random displacement models; with G. Stolz.  J. Spectr. Theory 1, No. 2, 123-153 (2011).

2012

  • Weak convergence of spectral shift functions for one-dimensional Schrödinger operators; with F. Gesztesy.  Math. Nachr. 285, No. 14-15, 1799-1838 (2012).
  • An abstract approach to weak convergence of spectral shift functions and applications to multi-dimensional Schrödinger operators; with F. Gesztesy. J. Spectr. Theory 2, No. 3, 225-266 (2012).

2013

  • Simplicity of eigenvalues in Anderson-type models; with G. Stolz and S. Naboko. Ark. Mat. 51, 157-183 (2013).
  • Weyl-Titchmarsh theory for Sturm-Liouville operators with distributional potentials; with J. Eckhardt, F. Gesztesy, and G. Teschl.  Opuscula Math. 33, No. 3, 467-563 (2013).
  • Inverse spectral theory for Sturm-Liouville operators with distributional potentials; with  J. Eckhardt, F. Gesztesy, and G. Teschl.  J. London Math. Soc. (2) 88, 801-828 (2013).
  • On square root domains for non-self-adjoint Sturm-Liouville operators; with F. Gesztesy and S. Hofmann.  Methods Funct. Anal. Topology, 19, No. 3, 227-259 (2013).

2014

  • Heat kernel bounds for elliptic partial differential operators in divergence form with Robin-type boundary conditions; with F. Gesztesy and M. Mitrea.  J. Anal. Math. 122, 229-287 (2014).
  • Boundary data maps and Krein's resolvent formula for Sturm-Liouville operators on a finite interval; with S. Clark, F. Gesztesy, and M. Zinchenko.  Oper. Matrices 8, No. 1, 1-71 (2014).
  • Supersymmetry and Schrödinger-type operators with distributional matrix-valued potentials; with J. Eckhardt, F. Gesztesy, and G. Teschl.  J. Spectr. Theory 4, No. 4, 715-768 (2014).

2015

  • Stability of square root domains associated with elliptic systems of PDEs on nonsmooth domains; with F. Gesztesy and S. Hofmann.  J. Differential Equation 258, 1749-1764 (2015). 
  • Heat kernel bounds for elliptic partial differential operators in divergence form with Robin-type boundary conditions II; with F. Gesztesy, M. Mitrea, and E. M. Ouhabaz.  Proc. Amer. Math. Soc. 143, No. 4, 1635-1649 (2015).
  • Inverse spectral problems for Schrödinger-type operators with distributional matrix-valued potentials; with J. Eckhardt, F. Gesztesy, A. Sakhnovich, and G. Teschl.  Differential Integral Equations 28, No. 5-6, 505-522 (2015).
  • On a problem in eigenvalue perturbation theory; with F. Gesztesy and S. Naboko.  J. Math. Anal. Appl. 428, No. 1, 295-305 (2015).
  • On factorizations of analytic operator-valued functions and eigenvalue multiplicity questions; with F. Gesztesy and H. Holden.  Integral Eq. and Operator Th. 82, No. 1, 61-94 (2015).
  • A Jost-Pais-type reduction of (modified) Fredholm determinants for semi-separable operators in infinite dimensions; with F. Gesztesy.  Appeared in Recent Advances in Schur Analysis and Stochastic Processes - A Collection of Papers Dedicated to Lev Sakhnovich, D. Alpay and B. Kirstein (eds.), Operator Theory:  Advances and Applications 244, 287-314 (2015).
  • Some applications of almost analytic extensions to operator bounds in trace ideals; with F. Gesztesy.  Methods Funct. Anal. Topology, 21, No. 2, 151-169 (2015).

2016

  • On stability of square root domains for non-self-adjoint operators under additive perturbations; with F. Gesztesy and S. Hofmann.  Mathematika 62, 111-182 (2016).
  • Dirichlet-to-Neumann maps, abstract Weyl-Titchmarsh M-functions, and a generalized index of unbounded meromorphic operator-valued functions; with J. Behrndt, F. Gesztesy, and H. Holden.  J. Differential Equations 261, 3551-3587 (2016).
  • Principal solutions revisited; with S. Clark and F. Gesztesy.  In Stochastic and Infinite Dimensional Analysis, C. C. Bernido, M. V. Carpio-Bernido, M. Grothaus, T. Kuna, M. J. Oliveira, and J. L. da Silva (eds.), Trends in Mathematics, Birkhäuser, Basel.

2017

  • On the index of meromorphic operator-valued functions and some applications; with J. Behrndt, F. Gesztesy, and H. Holden.  In Functional Analysis and Operator Theory for Quantum Physics, J. Dittrich, H. Kovarik, and A. Laptev (eds.), Series of Congress Reports, European Mathematical Society.