# Publications

Books | Articles in refereed journals | Submitted articles | Online articles | Other articles | Theses

## 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

Spectral Approximation of Banded Laurent Matrices with Localized Random Perturbations
Integral Equations and Operator Theory 42 (2002), 142-165

Invertibility at infinity of band-dominated operators in the space of essentially bounded functions
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

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

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

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

Sufficiency of Favard's condition for a class of band-dominated operators on the axis
Journal of Functional Analysis, 254 (2008), 1146-1159

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

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

On the integer points in a lattice polytope:

*n*-fold Minkowski sums and boundary Contributions to Algebra and Geometry, 52 (2011), 395-404
Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation
Numerical Methods for PDEs, 27 (2011), 31-69

Eigenvalue problem meets Sierpinski triangle: Computing the spectrum of a non-selfadjoint random operator
Operators and Matrices, 5 (2011), 633-648

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

Finite sections of random Jacobi operators
SIAM Journal on Numerical Analysis, 50 (2012), 287-306

The Main Diagonal of a Permutation Matrix
Linear Algebra and Applications, 439 (2013), 524-537

On the Spectra and Pseudospectra of a Class of non-self-adjoint Random Matrices and Operators
Operators and Matrices, 7 (2013), 739-775

An Affirmative Answer to a Core Issue on Limit Operator
Journal of Functional Analysis, 267 (2014), 901-917

Coburn's Lemma and the Finite Section Method for Random Jacobi Operators
Journal of Functional Analysis, 270 (2016), 802-841

Essential pseudospectra and essential norms of band-dominated operators
Journal of Mathematical Analysis and Applications, 437 (2016), 255-291

On the spectrum of operator families on discrete groups over minimal dynamical systems
Math. Z. 287, 993-1007 (2017)

Recycling Givens rotations for the efficient approximation of pseudospectra for band-dominated operators
Operators and Matrices, 11 (2017), 1171-1196

Variability Analysis of Via Crosstalk using Polynomial Chaos Expansion
2017 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO), 317-319, 2017

Note on spectra of non-selfadjoint operators over dynamical systems
Proc. Edinb. Math. Soc. 61 (2), 371-386 (2018)

Finite Sections of the Fibonacci Hamiltonian
Operator Theory: Advances and Applications, 268 (2018), 381-396

Feasibility of Uncertainty Quantification for Power Distribution Network Modeling Using PCE and a Contour Integral Method.
2018 Joint IEEE International Symposium on Electromagnetic Compatibility & Asia-Pacific Symposium on Electromagnetic Compatibility (20
18 Joint IEEE EMC & APEMC), Singapore

Circulant matrices: norm, powers, and positivity
Opuscula Math. 38, no. 6 (2018), 849-857

Finite sections: A functional analytic perspective on approximation methods
GAMM-Mitteilungen 41 (2018), no. 3, e201800013

## Submitted (and nearly submitted) articles

On Spectral Inclusion Sets and Computing the Spectra and Pseudospectra of Bounded Linear Operators
in preparation

Asymptotics of condition numbers and pseudospectra in an algebra of finite sections
in preparation

Novel Method for Error Estimation in Applications of Polynomial Chaos Expansion to Stochastic Modeling of Multi-Resonant Systems
submitted

De-Embedding and Embedding of Circular Ports for Simulation of 2D Photonic Crystals Using a Contour Integral Method
submitted

Applicability of Polynomial Chaos Expansion near Poles of Resonant Electric Systems
submitted

## Online articles (invited, refereed)

Pseudospectrum
Scholarpedia, 3(3):2680, 2008

## Other articles (preprints, conference proceedings)

Finite Sections in an Algebra of Convolution and Multiplication Operators on L

^{oo}(R) TU Chemnitz, Preprint 2000-6
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

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

Approximation of Pseudospectra on a Hilbert Space
Proceedings of ICNAAM 2015, AIP Conf. Proc. 1738, 4800 50, 2016

## 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