Publications	Talks	Projects & Grants

Publications

• Books

  Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method by Marko Lindner   Birkhäuser,  Basel - Boston - Berlin, 2006 Series: Frontiers in Mathematics ISBN: 3-7643-7766-6

  Limit Operators, Collective Compactness, and the Spectral Theory of Infinite Matrices by Simon N. Chandler-Wilde and Marko Lindner   Volume 210 (Number 989) of the series Memoirs of the American Mathematical Society AMS, Providence, Rhode Island, 2011.

• Articles in refereed journals

  • with Albrecht Böttcher and Mark Embree:
    Spectral Approximation of Banded Laurent Matrices with Localized Random Perturbations,
    Integral Equations and Operator Theory 42 (2002), 142-165.

  • with Bernd Silbermann:
    Invertibility at infinity of band-dominated operators in the space of essentially bounded functions,
    in Operator Theory: Advances and Applications, 147 (2003) - The Erhard Meister Memorial Volume, 295 - 323.

  • The Finite Section Method in the Space of Essentially Bounded Functions: An Approach using Limit Operators,
    Numerical Functional Analysis and Optimization 24 (2003), no. 7&8, 863-893.

  • with Vladimir S. Rabinovich and Steffen Roch:
    Finite sections of band operators with slowly oscillating coefficients,
    Linear Algebra and Applications, 390 (2004), 19-26.

  • Classes of Multiplication Operators and their Limit Operators,
    Zeitschrift für Analysis und ihre Anwendungen, 23 (2004), no. 1, 187-204.

  • with Simon Chandler-Wilde:
    Wave problems in unbounded domains: Fredholmness and the Finite Section Method,
    Contemp. Math., AMS, 440 (2007), 115-122.

  • with Simon Chandler-Wilde:
    Boundary integral equations on unbounded rough surfaces: Fredholmness and the Finite Section Method,
    Journal of Integral Equations and Applications, 20 (2008), no. 1, 13-48.

  • with Simon Chandler-Wilde:
    Sufficiency of Favard's condition for a class of band-dominated operators on the axis,
    Journal of Functional Analysis, 254 (2008), 1146-1159.

  • with Eric Heinemeyer and Roland Potthast:
    Convergence and numerics of a multi-section method for scattering by three-dimensional rough surfaces,
    SIAM Journal on Numerical Analysis, 46 (2008), 1780-1798.

  • Fredholmness and index of operators in the Wiener algebra are independent of the underlying space,
    Journal of Operators and Matrices, 2 (2008), 297-306.

  • Two stable modifications of the finite section method,
    Journal of Analysis, 16 (2008), 33-52.

  • with Simon Chandler-Wilde, Ivan Graham and Stephen Langdon:
    Condition Number Estimates for Combined Potential Boundary Integral Operators in Acoustic Scattering,
    Journal of Integral Equations and Applications, 21 (2009), 229-279.

  • A note on the spectrum of bi-infinite bi-diagonal random matrices,
    Journal of Analysis and Applications, 7 (2009), 269-278.

  • The finite section method and stable subsequences,
    Journal of Applied Numerical Mathematics, 60 (2010), 501-512.

  • with Steffen Roch:
    On the integer points in a lattice polytope: n-fold Minkowski sums and boundary,
    Contributions to Algebra and Geometry, 52 (2011), 395-404.

  • with Timo Betcke, Simon Chandler-Wilde, Ivan Graham and Stephen Langdon:
    Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation,
    Numerical Methods for PDEs, 27 (2011), 31-69.

  • with Simon Chandler-Wilde and Ratchanikorn Chonchaiya:
    Eigenvalue problem meets Sierpinski triangle: Computing the spectrum of a non-selfadjoint random operator,
    Operators and Matrices, 5 (2011), 633-648.

  • with Peter Bickel:
    Approximating the inverse of banded matrices by banded matrices with applications to probability and statistics,
    SIAM Journal on Probability Theory and Appl. 56 (2012), 1-20 and Teoriya Veroyatnostei i ee Primeneniya, 56, 100-122.

  • with Steffen Roch:
    Finite sections of random Jacobi operators,
    SIAM Journal on Numerical Analysis, 50 (2012), 287-306.

  • with Gilbert Strang:
    The Main Diagonal of a Permutation Matrix,
    Linear Algebra and Applications, 439 (2013), 524-537.

  • with Simon Chandler-Wilde and Ratchanikorn Chonchaiya:
    On the Spectra and Pseudospectra of a Class of non-self-adjoint Random Matrices and Operators,
    Operators and Matrices, 7 (2013), 739-775.

• Submitted (and nearly submitted) articles

  • with Markus Seidel:
    An Affirmative Answer to the Big Question on Limit Operators,
    submitted.

  • with Raffael Hagger and Markus Seidel:
    Essential pseudospectra and essential norms of band-dominated operators,
    in preparation.

  • with Simon Chandler-Wilde and Ratchanikorn Chonchaiya:
    On Spectral Inclusion Sets and Computing the Spectra and Pseudospectra of Bounded Linear Operators,
    in preparation.

  • with Simon Chandler-Wilde:
    Coburn's Lemma and the Finite Section Method for Random Jacobi Operators,
    in preparation.

• Online articles (invited, refereed)

  • with Albrecht Böttcher:
    Pseudospectrum, Scholarpedia, 3(3):2680, 2008.

• Other articles (preprints, conference proceedings)

  • with Bernd Silbermann:
    Finite Sections in an Algebra of Convolution and Multiplication Operators on L^oo(R),
    TU Chemnitz, Preprint 2000-6.

  • with Bernd Silbermann:
    An approach to the Finite Section Method in the space of essentially bounded functions using Limit Operators,
    TU Chemnitz, Preprint 2002-2.

  • Removing the »Nasty Condition« of Limit Operator Business in the Two Extremal Lebesgue Spaces,
    TU Chemnitz, Preprint 2003-7.

  • An Identification of Convolution Operators on Cones,
    TU Chemnitz, Preprint 2004-10.

  • with Simon Chandler-Wilde:
    On the Finite Section Method for Wave Problems in Unbounded Domains,
    Proceedings of ICNAAM2006, Hersonnisos, Crete, Greece,
    T.E. Simos, G. Psihoyios, Ch. Tsitouras (Eds.), WILEY-VCH Verlag, Weinheim, 2006.

  • The Finite Section Method and its Stable Subsequences,
    Proceedings of NumAn2008, Kalamata, Greece,
    G. Akrivis, E. Gallopoulos, A. Hadjidimos, I.S. Kotsireas, D. Noutsos, M.N. Vrahatis (Eds.), Peppas, Athens, 2008.

• Theses

  • Algebren von Toeplitzoperatoren auf der Viertelebene mit vom Grade Null homogenem Symbol
    Studienarbeit, under supervision of Prof. Bernd Silbermann,
    TU Chemnitz, May 1998.

  • Algebren, die von Toeplitzoperatoren mit homogener Erzeugerfunktion generiert werden
    Diplomarbeit (Dipl.-Math.), under supervision of Prof. Bernd Silbermann,
    TU Chemnitz, March 1999.

  • Limit Operators and Applications on the Space of Essentially Bounded Functions,
    Dissertation (Dr. rer. nat.), under supervision of Prof. Bernd Silbermann,
    TU Chemnitz, (submitted in April, defended in December) 2003.

  • Fredholm Theory and Stable Approximation of Band Operators and Their Generalisations,
    Habilitationsschrift (Dr. rer. nat. habil.),
    TU Chemnitz, (submitted in March, degree awarded in July) 2009 .

Talks

• Conferences ( = invited speaker, = plenary speaker)

  • Limit Operators and Applications,
    3rd International Conference on Boundary Integral Methods, Reading, England, September 2004.

  • Generalized Collective Compactness and Limit Operators,
    LMS Symposium on Operator Theory and Spectral Analysis, Durham, England, August 2005.

  • Wave problems in unbounded domains: Fredholmness and the Finite Section Method,
    Fluids and Waves, Memphis, USA, May 2006.

  • Wave problems in unbounded domains: Fredholmness and the Finite Section Method,
    MAFELAP 2006, Brunel (London), England, June 2006.

  • A boundary integral equation method for scattering by infinite rough surfaces,
    2nd British-French Waves Meeting, MATHmONDES2, Manchester, England, June 2006.

  • On the operator theory behind unbounded wave scattering problems,
    17th IWOTA, Seoul, Korea, July/August 2006.

  • On the finite section method for wave problems in unbounded domains,
    ICNAAM 2006, Hersonnisos, Greece, September 2006.

  • The multi-section method: Why rectangles are sometimes better than squares,
    22nd Biennal Conference on Numerical Analysis, Dundee, Scotland, June 2007.

  • Fredholmness of band-dominated Operators: Limit Operators and Collective Compactness,
    18th IWOTA, Potchefstroom, South Africa, June/July 2007.

  • Bounds on oscillatory integral operators from high frequency scattering,
    6th ICIAM, Zürich, Switzerland, July 2007.

  • The multi-section method: Why rectangles are sometimes better than squares,
    Waves 2007, Reading, England, July 2007.

  • Band-dominated Operators, Limit Operators and Applications,
    15th ICFIDCAA, Osaka, Japan, July/August 2007.

  • Fredholmness of operators in the Wiener algebra,
    Workshop on the Riemann-Hilbert Problem and Toeplitz Operators, Edinburgh, Scotland, September 2007.

  • Infinite matrices, their Fredholm properties and finite sections,
    International Conference of Functional Analysis and Applications, Kanyakumari, India, November 2007.

  • The spectrum of infinite matrices with two random diagonals,
    16th ICFIDCAA, Gyeongju, Korea, July/August 2008.

  • The finite section method and its stable subsequences,
    NumAn2008, Kalamata, Greece, September 2008.

  • Spectra of a class of non-selfadjoint random matrices from quantum mechanics,
    DMV Annual Meeting, Erlangen, Germany, September 2008.

  • A particular class of random matrices: Spectra and Pseudospectra,
    GAMM Annual Meeting, Gdansk, Poland, February 2009.

  • Spectra of a Class of non-selfadjoint Random Jacobi Matrices,
    2nd Najman Conference on Spectral Problems for Operators and Matrices, Dubrovnik, Croatia, May 2009.

  • Spectrum and essential spectrum of a class of infinite band matrices,
    17th ICFIDCAA, Ho Chi Minh City, Vietnam, August 2009.

  • Upper spectral bounds for band matrices and generalisations,
    1st Matrix and Operator Pencil Workshop, Reading, England, September 2009.

  • Spectra of Jacobi operators: Bounds and approximation,
    Functions and Operators FaO2010, Krakow, Poland, June 2010.

  • Spectra of Jacobi operators: Bounds and approximation,
    21st IWOTA, Berlin, Germany, July 2010.

  • Finite Sections and Spectra of Random Jacobi Operators,
    Workshop on Functional Analysis and Operator Theory, Altenberg, Germany, March 2011.

  • Finite Sections of Random Jacobi Operators,
    GAMM Annual Meeting, Graz, Austria, April 2011.

  • Spectra and Finite Sections of Random Operators,
    DMV Meeting, Cologne, Germany, September 2011.

  • Lecture series: Spectra and Finite Sections of Band Operators,
    Summer School on Applied Analysis, Chemnitz, Germany, September 2011.

  • On the integer points in a lattice polytope and their Minkowski sums,
    National Geometry Day, Chemnitz, Germany, December 2011.

  • Spektren endlicher und unendlicher zufälliger Jacobi-Matrizen,
    33. Norddeutsches Kolloquium über Angewandte Analysis und Numerische Mathematik, Rostock, Germany, May 2012.

  • Spectra of finite and infinite Jacobi Matrices,
    6th European Congress of Mathematics, Krakow, Poland, July 2012.

  • Spectra of finite and infinite Jacobi Matrices,
    Kick Off Meeting Maths@TUHH, TU Hamburg, Germany, July 2012.

  • Finite and Infinite Random Jacobi Matrices,
    Dissipative Spectral Theory Meeting, Cardiff, Wales, January 2013.

  • Where is the main diagonal of my bi-infinite matrix?
    Mathematical aspects of the physics with non-self-adjoint operators, Edinburgh, Scotland, March 2013.

• Invited Seminars

  • Limit Operators and Applications on the Space of Essentially Bounded Functions,
    Applied Maths and Numerical Analysis Seminar, Reading, England, January 2004.

  • Limit Operators and Applications in Operator Theory and Numerical Analysis,
    Functional Analysis Seminar, University of Oxford, England, January 2006.

  • Band-dominated Operators, Limit Operators and Applications,
    Mathematics Colloquium, Cardiff University, Wales, March 2007.

  • Infinite matrices, their spectra and Fredholm properties,
    Analysis Seminar, Newcastle University, England, October 2007.

  • Fredholm properties of band-dominated operators,
    London Analysis Seminar, King's College London, England, October 2007.

  • Spektral- und Fredholmtheorie einer grossen Klasse unendlicher Matrizen,
    Seminar Mathematische Physik, Chemnitz, October 2008.

  • Spektral- und Fredholmtheorie einer grossen Klasse unendlicher Matrizen,
    AG Mathematische Physik, Erlangen, October 2008.

  • Einige Klassen unendlicher Matrizen: Spektrum und stabile Approximation durch endliche Matrizen,
    Kolloquium des Instituts Mathematik und Informatik, Greifswald, November 2008.

  • Einige Klassen unendlicher Matrizen: Fredholm- und Spektraltheorie, Abschneideverfahren, Anwendungen,
    Kolloquium des Fachbereichs Mathematik und Informatik, Marburg, April 2009.

  • Klassen unendlicher Matrizen: Fredholm- und Spektraltheorie, Abschneideverfahren, Anwendungen,
    Institut für Mathematik, Lübeck, September 2009.

  • Zum Spektrum und wesentlichen Spektrum beschränkter Tridiagonaloperatoren,
    Mathematisches Institut, Jena, January 2010.

  • Zum Spektrum und wesentlichen Spektrum beschränkter Tridiagonaloperatoren,
    Fachbereich Mathematik, Darmstadt, January 2010.

  • Spectra of Jacobi operators: Analysis and approximation,
    Maxwell Institute, HWU Edinburgh, Scotland, February 2010.

  • Zum Spektrum von Jacobi-Operatoren: Analysis und Approximation,
    Oberseminar Analysis, Dresden, April 2010.

  • Spectra of Jacobi operators: Analysis and approximation,
    Kolloquium Modellierung, Numerik und Differentialgleichungen, TU Berlin, April 2010.

  • Abschneideverfahren in der Numerischen Analysis: Theorie und Anwendungen,
    Institut ICE, NTB Buchs, Switzerland, May 2010.

  • Zum Spektrum und wesentlichen Spektrum von Jacobioperatoren,
    Oberseminar Analysis und Spektraltheorie, Clausthal, June 2010.

  • Spectra of Jacobi operators: Analysis and approximation,
    Department of Mathematics, Universitat de Barcelona, Spain, June 2010.

  • Eigenwertprobleme in Theorie und Anwendung,
    Seminar Angewandte Mathematik, Hamburg-Harburg, December 2010.

  • Eigenwertprobleme in Theorie und Anwendung,
    Fachbereichskolloquium Mathematik, Zwickau, May 2011.

  • Spectra and Finite Sections of Jacobi Operators: Analysis and Approximation,
    Analysis Seminar, AGH Krakow, Poland, June 2011.

  • Finite Sections of Random Jacobi Operators,
    Applied Maths Seminar, Reading, England, June 2011.

  • Eigenwertprobleme und Projektionsverfahren,
    Analysis-Seminar, Freiberg, June 2011.

  • Eigenwertprobleme in Theorie und Anwendung,
    Kolloquium Analysis, Wuppertal, June 2011.

  • Über Sixpacks, Klumpen und Wurstkatastrophen,
    Tag der Mathematik, Uni Hamburg, November 2012.

Projects & Grants

• Wave Scattering in Unbounded Domains: Operator Algebra and Limit Operator Techniques (2005-2007)
  This project (led jointly with S. N. Chandler-Wilde) was supported by the EU with EUR 155k (Individual Marie-Curie Fellowship).

  The project was concerned with the mathematics (modelling, rigorous analysis, numerics) of wave scattering by unbounded surfaces and inhomogeneous regions and with the propagation of waves through unbounded inhomogeneous regions. Problems of this type arise widely in engineering applications and include radar wave scattering by ground and sea surfaces, propagation of acoustic and elastic (seismic) waves through the atmosphere, ocean, and earth, and scattering problems arising in electromagnetic optics, including the design of photonic crystals, and diffractive optical devices. Main results are: (i) a theory of invertibility and Fredholm properties (solvability, uniqueness & stability of solutions) of the corresponding (and more general) operator equations on unbounded domains; (ii) effective and stable numerical procedures for the solution of these equations. Our results and techniques find application in the treatment of direct (radar, sonar & acoustic noise barriers; atmospherical particle scattering) and indirect (mine detection; medical ultrasound; magnet tomography) scattering problems. Further research is funded by: BAE Systems, UK Met Office, UK Institute of Cancer Research and Schlumberger Ltd.

   

• Spectra, Fredholm Properties and Stable Approximation of Infinite Matrices (2008-2011)
  This project was supported by the EU with EUR 45k (Individual Marie-Curie Grant).

  The aim of the project was twofold: (i) To extend the theoretical results on the Fredholm- and spectral theory as well as on the numerical analysis of the rather general class of operator equations studied in the previous project. After the explicit (and practically relevant) description of the essential spectrum, the focus is now on the whole spectrum as well as on pseudospectra for very general non-selfadjoint operators. On the numerical side, we want to better understand and appropriately modify (in the case of non-stability) the truncation methods studied before. (ii) Our motivation for this research and the focus of the second part of this project is the application of our theory to concrete problems in mathematical physics and population biology. Here we mention the acoustic scattering problems from the first project and concrete problems from quantum physics such as the Anderson model and its non-selfadjoint versions by Hatano & Nelson, the randomly hopping particle model by Feinberg & Zee, and the study of discrete Schrödinger operators with random, almost periodic or slowly oscillating potential.