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) 425-4562
"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.
I am an associate professor in the Department of Mathematics at The University of Tennessee at Chattanooga.
Spectral theory of differential operators, functional analysis, and mathematical physics.
Articles in Refereed Journals and Proceedings:
26. Trace ideal properties of a class of integral operators, with F. Gesztesy, appeared in Integrable Systems and Algebraic Geometry, R. Donagi and T. Shaska (eds.), (London Mathematical Society Lecture Note Series). Cambridge: Cambridge University Press, 2020. (doi:10.1017/9781108773287)
25. On absence of threshold resonances for Schrödinger and Dirac operators, with F. Gesztesy, Discrete Contin. Dyn. Syst. Ser. S (2020). (doi: 10.3934/dcdss.2020243)
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).
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).
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.
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).
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.
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).
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).
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).
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).
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).
14. On a problem in eigenvalue perturbation theory, with F. Gesztesy and S. Naboko, J. Math. Anal. Appl. 428, No. 1, 295–305 (2015).
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).
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).
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).
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).
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).
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).
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).
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).
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).
4. Simplicity of eigenvalues in Anderson-type models, with G. Stolz and S. Naboko, Ark. Mat. 51, 157–183 (2013).
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).
2. Weak convergence of spectral shift functions for one-dimensional Schrödinger operators, with F. Gesztesy, Math. Nachr. 285, No. 14-15, 1799–1838 (2012).
1. Spectral properties of discrete random displacement models, with G. Stolz, J. Spectr. Theory 1, No. 2, 123–153 (2011).
3. On principal eigenvalues of biharmonic systems, with L. Kong.
2. On self-adjoint boundary conditions for singular Sturm–Liouville operators bounded from below, with F. Gesztesy and L. Littlejohn.
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)