**Günter Stolz **Department of
Mathematics

University of Alabama at Birmingham

Birmingham, Alabama 35294

E-mail: stolz@math.uab.edu

Fax: (205) 934-9025

Telephone: (205) 934-2154

- Expansions in Generalized Eigenfunctions of Selfadjoint
Operators (with Th. Poerschke and J. Weidmann), Math. Z.
**202**(1989), 397-408 - On the absolutely continuous spectrum of perturbed periodic
Sturm-Liouville operators, J. reine angew. Math.
**416**(1991), 1-23 - Bounded solutions and absolute continuity of Sturm-Liouville
operators, J. Math. Anal. Appl.
**169**(1992), 210-228 - Polynomial boundedness of eigensolutions and the spectrum of
Schrödinger operators (with A. M. Hinz), Math. Ann.
**294**(1992), 195-211 - On Eigenfunction Expansions and Scattering Theory (with Th.
Poerschke), Math. Z.
**212**(1993), 337-357 - Note to the paper by P. D. Hislop and S. Nakamura: Stark
Hamiltonian with unbounded random potentials, Rev. Math. Phys.
**5**(1993), 453-456 - Approximation of isolated eigenvalues of ordinary
differential operators (with J. Weidmann), J. reine angew. Math.
**445**(1993), 31-44 - Spectral theory of one-dimensional Schrödinger operators
with point interactions (with C. Shubin Christ), J. Math. Anal. Appl.
**184**(1994), 491-516 - Spectral theory for slowly oscillating potentials, I. Jacobi
matrices, manuscripta math.
**84**(1994), 245-260 - Stability of spectral types for Sturm-Liouville operators
(with R. del Rio and B. Simon), Mathematical Research Letters
**1**(1994), 437-450 - Singular spectrum for multidimensional Schrödinger operators
with potential barriers (with P. Stollmann), J. Operator Theory
**32**(1994), 91-109 - Absence of absolutely continuous spectra for
multidimensional Schrödinger operators with high barriers (with I. McGillivray
and P. Stollmann), Bull. London Math. Soc.
**27**(1995) 162-168 - Trace norm estimates for products of integral operators and
diffusion semigroups (with M. Demuth, P. Stollmann and J. A. van Casteren),
Integr. Equat. Oper. Th.
**23**(1995) 145-153 - Approximation of isolated eigenvalues of general singular
ordinary differential operators (with J. Weidmann), Results in Mathematics
**28**(1995) 345-358 - Localization for random Schrödinger operators with Poisson
potential, Ann. Inst. Henri Poincaré, Physique Théorique
**63**(1995) 297-314 - One-dimensional Schrödinger operators with local point
interactions (with D. Buschmann and J. Weidmann), J. reine angew. Math.
**467**(1995), 169-186 - Operators with singular continuous spectrum, V. Sparse
potentials (with B. Simon), Proc. Amer. Math. Soc.
**124**(1996), 2073-2080 - Spectral theory for slowly oscillating potentials, II.
Schrödinger operators, Math. Nachrichten
**183**(1997), 275-294 - Localization for Schrödinger operators with effective
barriers, to appear in J. Funct. Analysis
**146**(1997), 416-429 - Localization for random perturbations of periodic
Schrödinger operators (with W. Kirsch and P. Stollmann), Random Oper.\ and
Stoch. Equ.
**6**(1998), 153-180 - Anderson Localization for Random Schrödinger Operators with
Long Range Interactions (with W. Kirsch and P. Stollmann), Commun. Math. Phys.
**195**(1998), 495-507 - Non-Monotonic Random Schrödinger Operators: The Anderson
Model, J. Math. Anal. Appl.
**248**(2000), 173-183 - A Generalization of Gordon's Theorem and Applications to
Quasiperiodic Schrödinger Operators (with D. Damanik), Electronic J. Diff.
Equations
**55**(2000), 1-8 - Localization in one-dimensional random media: A scattering
theoretic approach (with R. Sims), Commun. Math. Phys.
**213**(2000), 575-597 - Two-Parameter Spectral Averaging and Localization for
Non-Monotonic Random Operators (with D. Buschmann), Trans. Amer. Math. Soc.
**353**(2000), 635-653 - Localization for one dimensional, continuum,
Bernoulli-Anderson models (with D. Damanik and R. Sims), Duke Math. J.
**114**(2002), 59-100 - The spectral minimum of the random displacement model (with J. Lott),
J. Comp. Appl. Math.
**148**(2002), 133-146 - Delocalization in random polymer models (with S. Jitomirskaya and
H. Schulz-Baldes), Commun. Math. Phys.
**233**(2003), 27-48 - Spectral theory for a class of periodically perturbed unbounded
Jacobi matrices: elementary methods (with J. Janas and S. Naboko), J. Comp. Appl.
Math.
**171**(2004), 265-276 - Localization for discrete one-dimensional random word models
(with D. Damanik and R. Sims), J. Funct. Anal.
**208**(2004), 423-445 - Absence of continuous spectral types for certain non-stationary
random models (with A. Boutet de Monvel and P. Stollmann), Ann. Henri Poincaré
**6**(2005), 309-326 - Localization for random unitary operators (with E. Hamza and
A. Joye), Lett. Math. Phys.
**75**(2006), 255-272 - Moment Analysis for Localization in Random Schrödinger Operators
(with M. Aizenman, A. Elgart, S. Naboko and J. H. Schenker), Invent. Math.
**163**(2006), 343-413 - Lower Transport Bounds for One-Dimensional Continuum Schrödinger
Operators
(with D. Damanik and D. Lenz), Math. Ann.
**336**(2006), 361-389 - Absolutely continuous spectrum of Schrödinger operators with
potentials slowly decaying inside a cone (with O. Safronov), J. Math. Anal. Appl.
**326**(2007), 192-208

- Entwicklung nach verallgemeinerten Eigenfunktionen von Schrödingeroperatoren, Dissertation, Universität Frankfurt 1989
- Expansions in Generalized Eigenfunctions of Schrödinger
Operators with Singular Potentials, in: Topics in Operator Theory, Ernst D.
Hellinger Memorial Volume, p. 353-372, Operator Theory, Vol.
**48**, Birkhäuser 1990 - Results in the spectral theory of Schrödinger operators with
wide potential barriers, pp.27-32, in: Operator Theory: Advances and
Applications, Vol.
**70**, Birkhäuser Verlag, Basel 1994 - Spectral theory of Schrödinger operators with potentials of infinite barriers type, Habilitationsschrift, Frankfurt 1994
- Localization for the Poisson Model, in: Operator Theory:
Advances and Applications, Vol.
**78**, p. 375-380, Birkhäuser 1995 - Sturm-Liouville Problems with an Infinite Number of Interior
Singularities (with W. N. Everitt, C. Shubin and Z. Zettl), pp.211-249, in:
Spectral theory and computational methods of Sturm-Liouville problems, Lecture
notes in pure and applied mathematics,
**191**, Marcel Dekker 1997 - Band edge localization in randomly perturbed crystals (with
W. Kirsch and P. Stollmann), pp.184-191, in: Differential Equations,
Asymptotic Analysis, and Mathematical Physics, Mathematical Research, Vol.
**100**, Akademie Verlag, Berlin 1997 - Sturm-Liouville Problems with an Infinite Number of Interior
Singularities (with W.~N.~Everitt, C.~Shubin and Z.~Zettl), pp.211-249, in:
Spectral theory and computational methods of Sturm-Liouville problems, Lecture
notes in pure and applied mathematics, Vol.
**191**, Marcel Dekker 1997 - Monotonicity versus Non-Monotonicity in Random Operators,
pp.365-371, in: Operator Theory: Advances and Applications, Vol.
**108**, Birkhäuser Verlag, Basel 1999 - Lyapunov exponents in continuum Bernoulli-Anderson models
(with D. Damanik and R. Sims), pp. 121-130, in: Operator Theory, Advances and
Applications, Vol.
**132**, Birkhäuser Verlag, Basel 2002 - Strategies in localization proofs for one-dimensional random
Schrödinger operators, Proc. Indian Acad. Science, J. Math. Sciences
**112**(2002), 229-243 - Fractional Moment Methods for Anderson Localization in the Continuum (with M. Aizenman, A. Elgart, S. Naboko and J. H. Schenker), pp. 619-625, in: XIVth International Congress on Mathematical Physics, World Sci. Publ., Hackensack, NJ, 2005

- Advances in differential equations and mathematical physics.
Proceedings of the 9th International Conference on Differential Equations and
Mathematical Physics held at the University of Alabama, Birmingham, AL, March
26-30, 2002. Edited by Yulia Karpeshina, Günter Stolz, Rudi Weikard and Yanni
Zeng. Contemporary Mathematics
**327**. American Mathematical Society, Providence, RI, 2003. xx+387 pp. - Operator Theory, Analysis and Mathematical Physics. Proceedings
of the International Conference held in Bedlewo, Poland, July 2004. Edited by
Jan Janas, Pavel Kurasov, Ari Laptev, Serguei Naboko and Günter Stolz, to appear
in Operator Theory: Advances and Applications
**174**, Birkhauser, May 2007

- Localization near fluctuation boundaries via fractional moments and applications (with A. Boutet de Monvel, S. Naboko and P. Stollmann), Preprint math-ph/0509061, to appear in J. Analyse Math.
- Positivity of Lyapunov exponents for Anderson-type models on two coupled strings (with H. Boumaza), Preprint math-ph/0611001
- Lyapunov Exponents for Unitary Anderson Models (with E. Hamza), Preprint math-ph/0611081

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