Title | Unique continuation principles and equidistribution properties of eigenfunctions |

DFG Code | Ve 253/6-1 |

GEPRIS | Projekt number 239209451 |

Principal Investigator | Prof. Dr. Ivan Veselić |

Researcher | M. Sc. Matthias Täufer |

Time | 2013-2016 |

Title: | Scale-free unique continuation principle for spectral projectors, eigenvalue lifting and Wegner estimates for random Schrödinger operators |

Authors: | I. Nakic, M. Täufer, M. Tautenhahn and I. Veselic |

Journal: | Anal. PDE,Vol. 11, No. 4, 1049-1081 |

Year: | 2018 (submitted in 2016) |

Preprint: | https://arxiv.org/abs/1609.01953 |

DOI: | 10.2140/apde.2018.11.1049 |

Title: | Scale-free and quantitative unique continuation for infinite dimensional spectral subspaces of Schrödinger operators |

Authors: | M. Täufer, and M. Tautenhahn |

Journal: | Commun. Pure Appl. Anal. 16, no. 5, 1719–1730. |

Year: | 2017 (submitted in 2016) |

Preprint: | arXiv:1609.07408 [math.AP] |

DOI: | 10.3934/cpaa.2017083 |

Title: | Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space |

Authors: | Norbert Peyerimhoff, Matthias Täufer, and Ivan Veselić |

Journal: | Nanosystems: Physics, Chemistry, Mathematics 08, no. 2, 216-230 |

Year: | 2017 |

Preprint: | http://arXiv.org/abs/1702.05299 |

DOI: | 10.17586/2220-8054-2017-8-2-216-230 |

Title: | Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations |

Authors: | Denis Borisov, Martin Tautenhahn, and Ivan Veselić |

Journal: | Journal of Mathematical Physics 58, 121502 |

Year: | 2017 |

Preprint: | http://arxiv.org/abs/1512.06347 |

DOI: | 10.1063/1.5017938 |

Title: | Harmonic Analysis and Random Schrödinger Operators |

Authors: | Matthias Täufer, Martin Tautenhahn, and Ivan Veselić |

Journal: | Operator Theory: Advances and Applications, 254, 223--255 |

Year: | 2016 |

Preprint: | http://arxiv.org/abs/1601.03585 |

DOI: | 10.1007/978-3-319-29992-1_11 |

Title: | Sampling inequality for $L^2$-norms of eigenfunctions of Schrödinger operators |

Authors: | Martin Tautenhahn, and Ivan Veselić |

Journal: | J. Stat. Phys., 164 (3), 616-620 |

Year: | 2016 |

Preprint: | arXiv:1504.00554 [math.AP] |

DOI: | 10.1007/s10955-016-1560-6 |

Title: | Wegner estimate for Landau-breather Hamiltonians |

Authors: | Matthias Täufer, and Ivan Veselić |

Journal: | J. Math. Phys., 57(7):072102, 8 |

Year: | 2016 |

Preprint: | arXiv:1607.00187 [math-ph] |

DOI: | 10.1063/1.4955029 |

Title: | Scale-free uncertainty principles and Wegner estimates for random breather potentials |

Authors: | Ivica Nakić, Matthias Täufer, Martin Tautenhahn, and Ivan Veselić |

Journal: | Comptes Rendus Mathematique,353 (10):919–923 |

Year: | 2015 |

Preprint: | http://arxiv.org/abs/1410.5273 |

DOI: | 10.1016/j.crma.2015.08.005 |

Title: | Conditional Wegner estimate for the standard random breather potential |

Authors: | Matthias Täufer, and Ivan Veselić |

Journal | J. Stat. Phys, Volume 161, Issue 4, pp 902-914 |

Year: | 2015 |

Preprint: | http://arxiv.org/abs/1509.03507 |

DOI: | 10.1007/s10955-015-1358-y |

Title: | Uncertainty relations and applications to the Schrödinger and heat conduction equations |

Speaker: | Ivan Veselic |

Occasion: | Summer school Spectral Theory, Differential Equations and Probability |

Institution/Location: | Universität Mainz |

Date: | September 2016 |

Title: | Wegner estimate for Landau Hamiltonians with random breather potential |

Speaker: | Matthias Täufer |

Occasion: | Summer school Spectral Theory, Differential Equations and Probability |

Institution/Location: | Universität Mainz |

Date: | September 2016 |

Title: | Quantitative unique continuation principles and application to control theory for the heat equation |

Speaker: | Martin Tautenhahn |

Occasion: | Summer school Spectral Theory, Differential Equations and Probability |

Institution/Location: | Universität Mainz |

Date: | September 2016 |

Title: | Quantitative unique continuation principles and application to control theory for the heat equation |

Speaker: | Martin Tautenhahn |

Occasion: | A trilateral German-Russian-Ukrainian summer school: Spectral Theory, Differential Equations and Probability |

Institution/Location: | Universität Mainz |

Date: | September 2016 |

Title: | Uncertainty relations and applications to the Schrödinger and heat conduction equations |

Speaker: | Ivan Veselic |

Occasion: | A trilateral German-Russian-Ukrainian summer school: Spectral Theory, Differential Equations and Probability |

Institution/Location: | Universität Mainz |

Date: | September 2016 |

Title: | Unique continuation principle and its absence on continuum space, on lattices and on quantum graphs |

Speaker: | Ivan Veselic |

Occasion: | NewMET 2016 |

Institution/Location: | WIAS Berlin |

Date: | July 2016 |

Title: | Scale-free unique continuation principles and application to the random breather model |

Speaker: | Matthias Täufer |

Occasion: | Operator Theory 26 |

Institution/Location: | Timisoara, Romania |

Date: | July 2016 |

Title: | Wegner estimate for the Landau-breather model |

Speaker: | Matthias Täufer |

Occasion: | International Workshop on PDEs: Analysis and modelling |

Institution/Location: | University of Zagreb, Croatia |

Date: | June 2016 |

Title: | Multiscale equidistribution estimates for Schr ̈odinger eigenfunctions |

Speaker: | Ivan Veselic |

Occasion: | nternational Workshop on PDEs: analysis and modelling |

Institution/Location: | University of Zagreb, Croatia |

Date: | June 2016 |

Title: | Quantitative unique continuation and Wegner estimate for random Schrödinger operators |

Speaker: | Martin Tautenhahn |

Occasion: | International Workshop on PDEs: Analysis and modelling |

Institution/Location: | University of Zagreb, Croatia |

Date: | June 2016 |

Title: | Quantitative uncertainty principles in harmonic analysis and mathematical physics |

Speaker: | Ivan Veselic |

Occasion: | 6th Croatian Mathematical Congress |

Institution/Location: | University of Zagreb, Croatia |

Date: | June 2016 |

Title: | Quantitative unique continuation principles and application to control theory |

Speaker: | Martin Tautenhahn |

Occasion: | 6th Croatian Mathematical Congress |

Institution/Location: | University of Zagreb, Croatia |

Date: | June 2016 |

Title: | Hadamard's three line theorem and Carleman estimates (Hadamardov teorem of tri pravca i Carlemanove ocjene) |

Speaker: | Ivan Veselic |

Occasion: | Colloquium of the Croatian Mathematical Society |

Institution/Location: | Zagreb University |

Date: | September 2015 |

Title: | Approximation and estimation of functions based on local data (Aproksimacija i ocjena funkcija na osnovu lokalnih podataka) |

Speaker: | Ivan Veselic |

Occasion: | Colloquium of the society of mathematicians and physicists |

Institution/Location: | Rijeka University, Department of Natural Sciences and Mathematics |

Date: | September 2015 |

Title: | Conditional Wegner Estimate for the Random Breather Model Matthias Täufer |

Speaker: | Matthias Täufer |

Occasion: | Fourth Najman Conference on spectral problems for operators and matrices |

Institution/Location: | Opatija, Croatia |

Date: | September 2015 |

Title: | Quantitative unique continuation for Schrödinger operators and applications |

Speaker: | Martin Tautenhahn |

Occasion: | Fourth Najman Conference on Spectral Problems for Operators and Matrices |

Institution/Location: | Opatija, Croatia |

Date: | September 2015 |

Title: | Uncertainty relations and applications (Relacije neodređenosti i primjene) |

Speaker: | Ivan Veselic |

Occasion: | Seminar of the Split mathematical society |

Institution/Location: | University of Split |

Date: | September 2015 |

Title: | Uncertainty relations and Wegner estimates for random breather potentials |

Speaker: | Ivan Veselic |

Occasion: | Workshop: Periodic and Other Ergodic Problems |

Institution/Location: | Isaac Newton Institue, Cambridge |

Date: | March 2015 |

Title: | Uncertainty principles and spectral analysis of Schroedinger operators |

Speaker: | Ivan Veselic |

Occasion: | Seminar Programme on Periodic and Ergodic Spectral Problems |

Institution/Location: | Isaac Newton Institue, Cambridge |

Date: | March 2015 |

Title: | Reconstruction and estimation of rigid functions based on local data |

Speaker: | Ivan Veselic |

Occasion: | Geometry and Topology Seminar |

Institution/Location: | Durham University |

Date: | March 2015 |

Title: | Quantitative Unique continuation estimates and Wegner bounds for random Schroedinger operators |

Speaker: | Ivan Veselic |

Occasion: | Mathematical Physics Seminar |

Institution/Location: | Department of Mathematics, Bristol University |

Date: | February 2015 |

Title: | Quantitative unique continuation and application to "non-linear" random Schrödinger operators |

Speaker: | Martin Tautenhahn |

Occasion: | Oberseminar Analysis und Zufall |

Institution/Location: | TU München, Germany |

Date: | January 2015 |

Title: | Quantitative unique continuation and Wegner estimate for random Schrödinger operators |

Speaker: | Martin Tautenhahn |

Occasion: | The Mathematics of Quantum Disordered Systems |

Institution/Location: | Euler International Mathematical Institute, St. Petersburg, Russia |

Date: | December 2014 |

Title: | Mini-Course: Harmonic Analysis and Random Schrödinger Operators |

Speaker: | Ivan Veselic |

Institution/Location: | Facultad de Matemáticas, Pontificia Universidad Católica de Chile |

Date: | November 2014 |

Title: | Quantitative unique continuation estimate and Wegner estimate for the standard random breather potential |

Speaker: | Ivan Veselic |

Occasion: | Plenary talk at the International Conference Spectral Theory and Mathematical Physics |

Institution/Location: | Pontificia Universidad Catolica de Chile |

Date: | November 2014 |

Title: | Unique countinuation principles, uncertainty relations and observability estimates for elliptic equations with multiscale structure |

Speaker: | Ivan Veselic |

Institution/Location: | Ecole des Ponts Paristech |

Date: | October 2014 |

Title: | Scale-free uncertainty principles and Wegner estimates for random breather potentials |

Speaker: | Ivan Veselic |

Occasion: | Seminar |

Institution/Location: | University Paris 6 |

Date: | October 2014 |

Title: | Uncertainty principles applied to observation and reconstruction of functions |

Speaker: | Ivan Veselic |

Occasion: | |

Institution/Location: | Plenaty talk meeting Mathematical Physics in Jena |

Date: | September 2014 |

Title: | Quantitative unique continuation and application to random Schrödinger operators |

Speaker: | Martin Tautenhahn |

Occasion: | Walkshop on Mathematical Physics and Partial Differential Equations |

Institution/Location: | TU Clausthal, Germany |

Date: | September 2014 |

Title: | Quantitative unique continuation and Wegner estimate for the random breather model |

Speaker: | Martin Tautenhahn |

Occasion: | Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) |

Institution/Location: | Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP), July 07-11 |

Date: | July 2014 |

Title: | Scale free unique continuation principle for linear combinations of eigenfunctions |

Speaker: | Martin Tautenhahn |

Occasion: | Chemnitz-Zagreb Workshop on Harmonic Analysis for PDE, Applications, and related topics |

Institution/Location: | TU Chemnitz |

Date: | July 2014 |

Title: | Uncertainty and unique continuation principles for the observation of eigenfunctions |

Speaker: | Ivan Veselic |

Occasion: | Oberseminar Analysis, Geometrie und Stochastik |

Institution/Location: | Universität Jena |

Date: | June 2014 |

Title: | Quantitative unique continuation for linear combinations of eigenfunctions and application to random Schrödinger operators |

Speaker: | Martin Tautenhahn |

Occasion: | Geometry and Analysis Seminar |

Institution/Location: | Friedrich Schiller Universität Jena |

Date: | May 2014 |

Title: | Unique continuation and equidistribution properties for eigenfunctions of elliptic operators |

Speaker: | Ivan Veselic |

Occasion: | Seminar Stochastic and Geometric Analysis |

Institution/Location: | Universität Bonn |

Date: | January 2014 |

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