### Contact Information:

Department of Mathematics

The University of Tennessee at Chattanooga

415 EMCS Building, Dept. 6956

615 McCallie Ave

Chattanooga, TN 37403, USA

** E-mail:** roger-nichols "at" utc "dot" edu

** Office:** EMCS 411

**Phone:** (423) 425-5856

"The best thing for being sad," replied Merlin, beginning to puff and blow, "is to learn something. That's the only thing that never fails. You may grow old and trembling in your anatomies, you may lie awake at night listening to the disorder of your veins, you may miss your only love, you may see the world about you devastated by evil lunatics, or know your honour trampled in the sewers of baser minds. There is only one thing for it then – to learn. Learn why the world wags and what wags it. That is the only thing which the mind can never exhaust, never alienate, never be tortured by, never fear or distrust, and never dream of regretting. Learning is the only thing for you. Look what a lot of things there are to learn." (T. H. White, The Once and Future King)

### NSF REU Site: Research Training for Undergraduates in Mathematical Analysis with Applications in Allied Fields

We gratefully acknowledge grant support from the National Science Foundation. This NSF REU grant enables us to organize a Mathematics REU Site in Chattanooga.

### 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.*Double operator integral methods applied to continuity of spectral shift functions*; with A. Carey, F. Gesztesy, G. Levitina, D. Potopov, and F. Sukochev. J. Spectr. Theory**6**, No. 4, 747–779 (2016).

**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.*Weak and vague convergence of spectral shift functions of one-dimensional Schrödinger operators with coupled boundary conditions*; with J. Murphy. Methods Funct. Anal. Topology**23**, No. 4, 378–403 (2017).**2018***On the global limiting absorption principle for massless Dirac operators*; with A. Carey, F. Gesztesy, J. Kaad, G. Levitina, D. Potapov, and F. Sukochev. Ann. Henri Poincaré**19**, No. 7, 1993–2019 (2018).