### Contact Information:

Department of Mathematics

The University of Tennessee at Chattanooga

Dept. 6956

615 McCallie Ave

Chattanooga, TN 37403, USA

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

** Office:** Lupton Hall 329

** Phone:** (423) 425-4562

"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.

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"I have come from Alabama: a fur piece. All the way from Alabama a-walking. A fur piece." ("Lena" in Light in August by William Faulkner)

### Research Interests:

Spectral theory of differential operators, functional analysis, and mathematical physics.

### Articles in Refereed Journals and Proceedings:

28. "On principal eigenvalues of biharmonic systems," with L. Kong, *Commun. Pure Appl. Anal.*, doi: 10.3934/cpaa.2020254. [PDF]

27. "On self-adjoint boundary conditions for singular Sturm–Liouville operators bounded from below," with F. Gesztesy and L. Littlejohn, *J. Differential Equations* **269**, 6448–6491 (2020). [PDF]

26. "Trace ideal properties of a class of integral operators," with F. Gesztesy, appeared
in *Integrable Systems and Algebraic Geometry. Volume 1*, R. Donagi and T. Shaska (eds.), *London Math. Soc. Lecture Note Ser.* **458**, Cambridge University Press, Cambridge, UK, 2020, pp. 13–37. [PDF]

25. "On absence of threshold resonances for Schrödinger and Dirac operators," with F. Gesztesy, *Discrete Contin. Dyn. Syst. Ser. S* **13**(12), 3427–3460 (2020). [PDF]

24. "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). [PDF]

23. "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). [PDF]

22. "On the index of meromorphic operator-valued functions and some applications," with J. Behrndt, F. Gesztesy, and H. Holden, appeared in *Functional Analysis and Operator Theory for Quantum Physics*, J. Dittrich, H. Kovarik, and A. Laptev (eds.), *Series of Congress Reports*, European Mathematical Society, Zürich, 2017. [PDF]

21. "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). [PDF]

20. "Principal solutions revisited,"* *with S. Clark and F. Gesztesy, appeared 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, 2016. [PDF]

19. "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). [PDF]

18. "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). [PDF]

17. "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). [PDF]

16. "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). [PDF]

15. "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). [PDF]

14. "On a problem in eigenvalue perturbation theory,"* *with F. Gesztesy and S. Naboko, *J. Math. Anal. Appl.* **428**, No. 1, 295–305 (2015). [PDF]

13. "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). [PDF]

12. "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). [PDF]

11. "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). [PDF]

10. "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). [PDF]

9. "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). [PDF]

8. "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). [PDF]

7. "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). [PDF]

6. "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). [PDF]

5. "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). [PDF]

4. "Simplicity of eigenvalues in Anderson-type models," with G. Stolz and S. Naboko, *Ark. Mat.* **51**, 157–183 (2013). [PDF]

3. "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). [PDF]

2.** "**Weak convergence of spectral shift functions for one-dimensional Schrödinger operators,"
with F. Gesztesy, *Math. Nachr.* **285**, No. 14-15, 1799–1838 (2012). [PDF]

1.** "**Spectral properties of discrete random displacement models," with G. Stolz, *J. Spectr. Theory* **1**, No. 2, 123–153 (2011). [PDF]

### Preprints:

5. "The Krein–von Neumann extension revisited," with G. Fucci, F. Gesztesy, K. Kirsten, L. Littlejohn, and J. Stanfill.

4. "Spectral analysis of a rod with a sharp end: does a black hole make sound?," with B. Belinskiy and D. Hinton.

3. "The product formula for regularized Fredholm determinants," with T. Britz, A. Carey, F. Gesztesy, F. Sukochev, and D. Zanin.

2. "A survey of some norm inequalities," with F. Gesztesy and J. Stanfill.

1. "Explicit Krein resolvent identities for singular Sturm–Liouville operators with applications to Bessel operators," with S. B. Allan, J. H. Kim, G. Michajlyszyn, and D. Rung.

"This went on at any odd hour, if necessary, with a floor rug over his shoulders, with the fine quiet of the scholar which is nearest of all things to heavenly peace." (F. Scott Fitzgerald, Tender is the Night)