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

List of Publications
A. Articles in refereed journals
  1. Expansions in Generalized Eigenfunctions of Selfadjoint Operators (with Th. Poerschke and J. Weidmann), Math. Z. 202 (1989), 397-408
  2. On the absolutely continuous spectrum of perturbed periodic Sturm-Liouville operators, J. reine angew. Math. 416 (1991), 1-23
  3. Bounded solutions and absolute continuity of Sturm-Liouville operators, J. Math. Anal. Appl. 169 (1992), 210-228
  4. Polynomial boundedness of eigensolutions and the spectrum of Schrödinger operators (with A. M. Hinz), Math. Ann. 294 (1992), 195-211
  5. On Eigenfunction Expansions and Scattering Theory (with Th. Poerschke), Math. Z. 212 (1993), 337-357
  6. Note to the paper by P. D. Hislop and S. Nakamura: Stark Hamiltonian with unbounded random potentials, Rev. Math. Phys. 5 (1993), 453-456
  7. Approximation of isolated eigenvalues of ordinary differential operators (with J. Weidmann), J. reine angew. Math. 445 (1993), 31-44
  8. Spectral theory of one-dimensional Schrödinger operators with point interactions (with C. Shubin Christ), J. Math. Anal. Appl. 184 (1994), 491-516
  9. Spectral theory for slowly oscillating potentials, I. Jacobi matrices, manuscripta math. 84 (1994), 245-260
  10. Stability of spectral types for Sturm-Liouville operators (with R. del Rio and B. Simon), Mathematical Research Letters 1 (1994), 437-450
  11. Singular spectrum for multidimensional Schrödinger operators with potential barriers (with P. Stollmann), J. Operator Theory 32 (1994), 91-109
  12. 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
  13. 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
  14. Approximation of isolated eigenvalues of general singular ordinary differential operators (with J. Weidmann), Results in Mathematics 28 (1995) 345-358
  15. Localization for random Schrödinger operators with Poisson potential, Ann. Inst. Henri Poincaré, Physique Théorique 63 (1995) 297-314
  16. One-dimensional Schrödinger operators with local point interactions (with D. Buschmann and J. Weidmann), J. reine angew. Math. 467 (1995), 169-186
  17. Operators with singular continuous spectrum, V. Sparse potentials (with B. Simon), Proc. Amer. Math. Soc. 124 (1996), 2073-2080
  18. Spectral theory for slowly oscillating potentials, II. Schrödinger operators, Math. Nachrichten 183 (1997), 275-294
  19. Localization for Schrödinger operators with effective barriers, to appear in J. Funct. Analysis 146 (1997), 416-429
  20. Localization for random perturbations of periodic Schrödinger operators (with W. Kirsch and P. Stollmann), Random Oper.\ and Stoch. Equ. 6 (1998), 153-180
  21. Anderson Localization for Random Schrödinger Operators with Long Range Interactions (with W. Kirsch and P. Stollmann), Commun. Math. Phys. 195 (1998), 495-507
  22. Non-Monotonic Random Schrödinger Operators: The Anderson Model, J. Math. Anal. Appl. 248 (2000), 173-183
  23. A Generalization of Gordon's Theorem and Applications to Quasiperiodic Schrödinger Operators (with D. Damanik), Electronic J. Diff. Equations 55 (2000), 1-8
  24. Localization in one-dimensional random media: A scattering theoretic approach (with R. Sims), Commun. Math. Phys. 213 (2000), 575-597
  25. Two-Parameter Spectral Averaging and Localization for Non-Monotonic Random Operators (with D. Buschmann), Trans. Amer. Math. Soc. 353 (2000), 635-653
  26. Localization for one dimensional, continuum, Bernoulli-Anderson models (with D. Damanik and R. Sims), Duke Math. J. 114 (2002), 59-100
  27. The spectral minimum of the random displacement model (with J. Lott), J. Comp. Appl. Math. 148 (2002), 133-146
  28. Delocalization in random polymer models (with S. Jitomirskaya and H. Schulz-Baldes), Commun. Math. Phys. 233 (2003), 27-48
  29. 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
  30. Localization for discrete one-dimensional random word models (with D. Damanik and R. Sims), J. Funct. Anal. 208 (2004), 423-445
  31. 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
  32. Localization for random unitary operators (with E. Hamza and A. Joye), Lett. Math. Phys. 75 (2006), 255-272
  33. 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
  34. Lower Transport Bounds for One-Dimensional Continuum Schrödinger Operators (with D. Damanik and D. Lenz), Math. Ann. 336 (2006), 361-389
  35. Absolutely continuous spectrum of Schrödinger operators with potentials slowly decaying inside a cone (with O. Safronov), J. Math. Anal. Appl. 326 (2007), 192-208
B. Contributions to conference proceedings and others
  1. Entwicklung nach verallgemeinerten Eigenfunktionen von Schrödingeroperatoren, Dissertation, Universität Frankfurt 1989
  2. 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
  3. 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
  4. Spectral theory of Schrödinger operators with potentials of infinite barriers type, Habilitationsschrift, Frankfurt 1994
  5. Localization for the Poisson Model, in: Operator Theory: Advances and Applications, Vol. 78, p. 375-380, Birkhäuser 1995
  6. 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
  7. 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
  8. 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
  9. Monotonicity versus Non-Monotonicity in Random Operators, pp.365-371, in: Operator Theory: Advances and Applications, Vol. 108, Birkhäuser Verlag, Basel 1999
  10. 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
  11. Strategies in localization proofs for one-dimensional random Schrödinger operators, Proc. Indian Acad. Science, J. Math. Sciences 112 (2002), 229-243
  12. 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
C. Books edited
  1. 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.
  2. 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
D. Preprints
  1. 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.
  2. Positivity of Lyapunov exponents for Anderson-type models on two coupled strings (with H. Boumaza), Preprint math-ph/0611001
  3. Lyapunov Exponents for Unitary Anderson Models (with E. Hamza), Preprint math-ph/0611081

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