Recent preprints/publications:

2023

B. Güneysu, S. Pigola, P. Stollmann and G. Veronelli: A new notion of subharmonicity on locally smoothing spaces, and a conjecture by Braverman, Milatovic, Shubin
arXiv: 2302.09423

2022

A. BenAmor, B. Güneysu and P. Stollmann: Essential spectrum and Feller type properties
arXiv: 2204.09390
article: here

M. Hansmann, C. Rose and P. Stollmann: Bounds on the first Betti number - an approach via Schatten norm estimates on semigroup differences. J. Geom. Anal. 32 (2022), no. 4, Paper No. 115, 17 pp.
arXiv: 1810.12205

2021

2019

D. Lenz and P. Stollmann: On the decomposition principle and a Persson type theorem for general regular Dirichlet forms. Journal of Spectral Theory, Volume 9, Issue 3, 2019, pp. 1089–1113 DOI: 10.4171/JST/272
arXiv: 1705.103981801.09279

2018

A. Böttcher, D. Potts, P. Stollmann and D. Wenzel (Eds): The Diversity and Beauty of Applied Operator Theory, Springer 2018.
LINK

C. Rose and P. Stollmann: Manifolds with Ricci curvature in the Kato class: heat kernel bounds and applications.
arXiv: 1804.04094

D. Lenz, M. Schmidt and P. Stollmann: Topological Poincar\'{e} type inequalities and lower bounds on the\00 infimum of the spectrum for graphs.
arXiv: 1801.09279

2017

C. Rose and P. Stollmann: The Kato class on compact manifolds with integral bounds on the negative part of Ricci curvature. Proc. Amer. Math. Soc. 145 (2017), no. 5, 2199–2210.
arXiv: 1601.07441

2016

2014

D. Lenz, C. Seifert and P. Stollmann: Zero measure Cantor spectra for continuum one-dimensional quasicrystals. J. Differential Equations 256 (2014), no. 6, 1905–1926.
arXiv: 1308.3431

Reza Samavat, Peter Stollmann, Ivan Veselic: Lifshitz asymptotics for percolation Hamiltonians. Bull. Lond. Math. Soc. 46 (2014), no. 6, 1113–1125.
arXiv: 1308.1842

2013

P. Exner, C. Seifert and P. Stollmann: Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees. Ann. Henri Poincaré 15 (2014), no. 6, 1109–1121.  
arXiv: 1305.0656

2011

J.J. Perez and P. Stollmann: Essential selfadjointness, generalized eigenforms, and spectra for the $\dbar$-Neumann problem on $G$-manifolds . Journal of Functional Analysis 261 (2011), pp. 2717-2740   DOI information: 10.1016/j.jfa.2011.07.010    .pdf
arXiv: 1101.1863
ESI-Preprint #2301

2010

M. Krishna and P. Stollmann: Direct integrals and spectral averaging J. Operator Theory, 69(1), 101--107    .pdf
arXiv: 1011.1920

J.J. Perez and P. Stollmann: Heat kernel estimates for the Neumann Laplacian on G-manifolds. manuscripta math. DOI 10.1007/s00229-011-0496-z    .pdf
arXiv: 1009.4900
ESI-Preprint #2334

Anne Boutet de Monvel, Victor Chulaevsky, Peter Stollmann, Yuri Suhov : Anderson localization for a multi-particle model with alloy-type external potential.    .pdf
arXiv: 1004.1300

Steffen Klassert, Daniel Lenz, Peter Stollmann: Delone measures of finite local complexity and applications to spectral theory of one-dimensional continuum models of quasicrystals.    Discrete and Continuous Dynamical Systems (DCDS-A), vol. 29 (4), 2011 .pdf
arXiv: 1003.3574

P. Müller and P. Stollmann: Percolation Hamiltonians.    in Random Walks, Boundaries and Spectra, edited by D. Lenz, F. Sobieczky and W. Woess, Progress in Probability, vol. 64, 235--258 (Springer, Basel, 2011) .pdf
arXiv: 1002.5000

2009

D. Lenz, P. Stollmann and I. Veselic: Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms.To appear in: OTAMP 2008 proceedings; eprint arXiv: 0909.1107

A. Boutet de Monvel, V. Chulaevsky, P. Stollmann, Y. Suhov: Anderson localization in a two-particle continuous model with an alloy-type external potential.
arXiv: 0907.1459
Journal of Statistical Physics. 138. 2010, 4-5, S. 553 - 566

P. Stollmann: From uncertainty principles to Wegner estimates.    Math. Phys. Anal. Geom. 13 (2010), no. 2, 145-157 .pdf

A. Boutet de Monvel, D. Lenz and P. Stollmann: AN UNCERTAINTY PRINCIPLE, WEGNER ESTIMATES AND LOCALIZATION NEAR FLUCTUATION BOUNDARIES.
arXiv: 0905.2845 Math. Z. online first, DOI 10.1007/s00209-010-0756-8, .pdf

P. Stollmann: A dual characterization of length spaces with application to Dirichlet metric spaces. arXiv: 0903.3544 ,   Studia Math. 198 (2010), no. 3, 221-233    .pdf

D. Lenz, P. Stollmann and D. Wingert: Compactness of Schrödinger semigroups. . Math. Nachr. 283, No. 1, 94-103 (2010) .pdf

2008

A. Boutet de Monvel, V. Chulaevsky, P. Stollmann and Y. Suhov: Wegner-type bounds for a two-particle continuous Anderson model with an alloy-type external potential. eprint arXiv:0812.2621,   J. Stat. Phys. 138 (2010), no. 4-5, 553–566 .pdf

D. Lenz, P. Stollmann and I. Veselic: The Allegretto-Piepenbrink theorem for strongly local Dirichlet forms. eprint arXiv:0811.2135,   final form Documenta Math., 14 (2009), 167--189 .pdf

D. Lenz, C. Schubert and P. Stollmann: Eigenfunction expansion for Schrödinger operators on metric graphs. Integr. equ. oper. theory, 62 (2008), 541--553    .pdf

2007

A. Boutet de Monvel, D. Lenz and P. Stollmann: Sch'nol's Theorem For Strongly Local Forms. Israel. J. 173 (2009), 189 -- 211, eprint arXiv:math-ph/0780.1501,   .pdf

P. Exner, M. Helm and P. Stollmann: Localization on a quantum graph with a random potential on the edges. Rev. Math. Phys. 19(9) (2007), 923 -- 939   eprint arXiv:math-ph/0612087,   .pdf

P. Müller and P. Stollmann: Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs. J. Funct. Anal. 252(1) (2007), 233--246    eprint arXiv math-ph/0506053  .pdf

2006

Boutet de Monvel, A. ; Naboko, S. ; Stollmann, P. ; Stolz, G.: Localization near fluctuation boundaries via fractional moments and applications. J. Anal. Math. 100 (2006), 83--116  .pdf

Karmann, Peter; Römer, Rudolf A.; Schreiber, Michael; Stollmann, Peter: Fine structure of the integrated density of states for Bernoulli-Anderson models. Parallel algorithms and cluster computing, 267--280, Lect. Notes Comput. Sci. Eng., 52,Springer, Berlin, 2006. .pdf

Lenz, Daniel; Stollmann, Peter: Generic subsets in spaces of measures and singular continuous spectrum. Mathematical physics of quantum mechanics, 333--341, Lecture Notes in Phys., 690,Springer, Berlin, 2006.    ISSN 1616-6361  .pdf

Lenz, Daniel; Stollmann, Peter: Generic sets in spaces of measures and generic singular continuous spectrum for Delone Hamiltonians. Duke Math. J. 131 (2006), no. 2, 203--217. .pdf

Hundertmark, Dirk; Killip, Rowan; Nakamura, Shu; Stollmann, Peter; Veseli\'c, Ivan: Bounds on the spectral shift function and the density of states. Comm. Math. Phys. 262 (2006), no. 2, 489--503. ISSN: 0010-3616 (Paper) 1432-0916 (Online)   .pdf

Klassert, Steffen; Lenz, Daniel; Peyerimhoff, Norbert; Stollmann, Peter: Elliptic operators on planar graphs: unique continuation for eigenfunctions and nonpositive curvature. Proc. Amer. Math. Soc. 134 (2006), no. 5, 1549--1559 (electronic).   ISSN 1088-6826 (e) ISSN 0002-9939 (p)  .pdf

2005 - 2001

A. Boutet de Monvel, P. Stollmann and G. Stolz: Absence of continuous spectral types for certain nonstationary random Schrödinger operators. Ann. Henri Poincar'e 6(2), 309--326(2005),  .pdf

S. Böcker, W. Kirsch and P. Stollmann: Spectral theory for nonstationary random models. In: Interacting stochastic systems, 103--117, Springer, Berlin, 2005.  .pdf

P. Stollmann: Localization and delocalization for nonstationary models. In: Multiscale Methods in Quantum Mechanics: Theory and Experiment,    P. Blanchard and G. Dell'Antonio, eds.   .pdf

D. Lenz and P. Stollmann: An ergodic theorem for Delone dynamical systems and existence of the integrated density of states. Journal d'Analyse Mathematique, 97 1--24(2005),    .pdf

D. Lenz and P. Stollmann: Aperiodic order and quasicrystals: spectral properties. Ann. Inst. Henri Poincare, 4 787 -- 796 (2003),    .ps , .pdf

S. Klassert, D. Lenz and P. Stollmann: Delone dynamical systems: ergodic features and applications. In: Quasicrystals, Structure and Physical Properties, H.-R. Trebin (ed.), Wiley-VCH, Berlin 2003   .ps , .pdf

S. Klassert, D. Lenz and P. Stollmann: Discontinuities of the integrated density of states for random operators on Delone sets. Comm. Math. Phys., 241, 235 - 243 (2003),   .ps , .pdf

D. Lenz and P. Stollmann: Algebras of random operators associated to Delone dynamical systems. Math. Phys. Anal. Geom., 6(3), 269 - 290 (2003)   .pdf

D. Lenz and P. Stollmann: Delone dynamical systems and associated random operators. In: Proc. OAMP, Constanta 2001, eds. Combes et al, Theta Foundation, 2003
  .ps , .pdf

A. Boutet de Monvel and P. Stollmann: Eigenfunction expansions for generators of Dirichlet forms. J. Reine Angew. Math., 561, 131 - 144 (2003)   .ps
.pdf

A. Boutet de Monvel and P. Stollmann: Dynamical localization for continuum random surface models. Arch. Math., 80(1), 87 - 97 (2003)   .ps , .pdf

D. Lenz and P. Stollmann: Quasicrystals, aperiodic order, and groupoid von Neumann algebras. C.R. Acad. Sci. Paris, Ser. I, 334, 1131 -- 1136 (2002)    .ps , .pdf

P. Stollmann: Caught by disorder: bound states in random media. Progress in Math. Phys., vol 20, Birkhäuser, Boston, 2001    look here

D. Damanik and P. Stollmann: Multi-scale analysis implies strong dynamical localization. Geom. Funct. Anal., 11 (1), 11--29 (2001)   .ps , .pdf

2000 - 1996

V. Liskevich and P. Stollmann: Schrödinger operators with singular complex potentials as generators: existence and stability. Semigroup Forum, 60 (3), 337--343 (2000)     .ps , .pdf

P. Stollmann: Wegner estimates and localization for continuum Anderson models with some singular distributions. Arch. Math. 75 (4), 307--311 (2000)    .ps

F. Kleespies and P. Stollmann: Lifshitz Asymptotics and Localization for Random Quantum Waveguides. Rev. Math. Phys., 12 (10), 1345--1365 (2000)    .pdf, .ps

B. Metzger and P. Stollmann: Heat kernel estimates on weighted graphs. Bull. London Math. Soc., 32 (4), 477--483 (2000)    .ps

P. Stollmann: Lifshitz Asymptotics via linear coupling of disorder. Math. Phys. Anal. Geom., 2(3), 279 - 289 (1999)    .pdf , .ps

W. Kirsch, G. Stolz and P. Stollmann: Anderson localization for random Schrödinger operators with long range interactions. Comm. Math. Phys., 195, 495 -- 507 (1998)    .ps , .pdf

W. Kirsch, G. Stolz and P. Stollmann: Localization for random perturbations of periodic Schrödinger operators. Random Oper. Stochastic Equations, 6, 241 -- 268 (1998)     .ps
.pdf

E.M. Ouhabaz and P. Stollmann: Stability of the essential spectrum of second-order complex elliptic operators. J. Reine Angew. Math., 500, 113--126 (1998)     .ps , .pdf

P. Stollmann: Localization for random perturbations of anisotropic periodic media. Israel J. Math., 107, 125 -- 139 (1998)   .ps, .pdf

W. Kirsch, P. Stollmann and G. Stolz: Band edge localization in randomly perturbed crystals. In: Differential Equations, Asymptotic Analysis, and Mathematical Physics, eds. Michael Demuth, Bert-Wolfgang Schulze, Akademie Verlag, Berlin 1997, p.184-191     .ps

E.M. Ouhabaz, P. Stollmann, K.Th. Sturm and J. Voigt: The Feller Property for Absorption Semigroups. J. Funct. Anal., 138 351 --378 (1996)     .ps , .pdf

W. Kirsch, P. Stollmann and G. Stolz: Anderson localization for random Schrödinger operators with long range interactions. Preprint 1996, old version,   .ps

P. Stollmann and J. Voigt: Perturbation of Dirichlet forms by measures. Potential Analysis 5, 109 - 138 (1996)    .pdf

1995 and earlier

P. Stollmann and G. Stolz: Singular spectrum for multidimensional Schrödinger operators with potential barriers. J. Operator Theory 32 (1995), 91 -- 109   PS

M. Demuth, P. Stollmann, G. Stolz and J. van Casteren: Trace norm estimates for products of integral operators and diffusion semigroups. Integr. Equat. Oper. Th. 23 (1995), 145--153   PDF

P. Stollmann: A convergence theorem for Dirichlet forms with applications to boundary value problems with varying domains. Math. Z. 219 (1995), 275--287   .pdf

I.McGillivray, P. Stollmann and G. Stolz: Absence of absolutely continuous spectra for multidimensional Schrödinger operators with high barriers. Bull. London Math. Soc. 27 (1995), 162--168   .pdf , .ps

Stollmann, P.: Convergence of Schrödinger operators with varying Dirichlet boundary conditions. in Operator Theory: Advances and Applications, Vol. 78, Birkhäuser Verlag, Basel 1995  .pdf

Stollmann, P.: Störungstheorie von Dirichletformen mit Anwendungen auf Schrödinger Operatoren. Habilitationsschrift(1994): Universität Frankfurt  .ps

Stollmann, P.: Scattering by obstacles of finite capacity. J. Funct. Anal. 121 (1994): 416 -- 425  .pdf

Stollmann, P.: Trace ideal properties of perturbed Dirichlet semigroups. in Operator Theory: Advances and Applications, Vol. 70, Birkhäuser Verlag, Basel 1993, pp. 153 -- 158  .ps

Stollmann, P.: Closed ideals in Dirichlet spaces. Potential Anal. 2(3) (1993): 263--268  .pdf

Stollmann, P.: Smooth perturbations of regular Dirichlet forms. {Proc. Amer. Math. Soc.116(3) (1992): 747--752  .pdf

Stollmann, P.: Representation of operators by kernels. Collect. Math. 42(3) (1991): 285-292  .pdf

Stollmann, P.: Admissible and regular potentials for Schrödinger forms. J. Operator Theory 18(1) (1987): 139-151.  .pdf

Stollmann, P. and J. Voigt: A regular potential which is nowhere in L1. Lett. Math. Phys. 9 (1985), 227 -- 230  .pdf