糖心视频

Publications

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Integral Equations and Operator Theory (2026)

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Journal of Computational and Applied Mathematics Vol 484 (2026)

, Lamb Wilson,

PDEs, Operator Theory, and Mathematical Physics A Tribute to the Scientific Work of Rainer Picard on the Occasion of His 80th Birthday (2025) (2025)

, Woracek Harald

Proceedings of the Royal Society of Edinburgh: Section A Mathematics Vol 155, pp. 1431-1491 (2025)

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Domain Decomposition Methods in Science and Engineering XXVIII 28th International Conference on Domain Decomposition Methods Lecture Notes in Computational Science and Engineering (2025)

, Pruckner Raphael, Woracek Harald

Annali della Scuola Normale Superiore di Pisa, Classe di Scienze Vol 25, pp. 2259-2330 (2024)

Research Interests

• differential operators, in particular elliptic PDOs and differential operators with singular coefficients
• functions whose values are operators on a Banach space for the study of spectral problems that depend nonlinearly on the eigenvalue parameter
• block operator matrices, i.e. matrices whose entries are operators between Banach spaces, with applications to systems of differential equations
• inverse problems: in particular, mathematical models for non-destructive testing with ultrasonic waves, inverse spectral problems for differential equations with singular coefficients
• operator semigroups and evolution equations, in particular, coagulation-fragmentation equations
• spaces with indefinite inner products and their use in singular perturbations and inverse spectral theory

Professional Activities

Editorial board member

2016

Editorial board member

2/2014

Visiting researcher

7/2010

Keynote/plenary speaker

2010

Organiser

6/2009

Invited speaker

2009

Projects

Langer, Matthias (Principal Investigator) Dolean Maini, Victorita (Co-investigator) Fry, Mark (Research Co-investigator)

01-Jan-2021 - 01-Jan-2025

Majumdar, Apala (Principal Investigator) Langer, Matthias (Co-investigator) McLauchlan, Sophie (Research Co-investigator)

Ferronematics in Confinement - Modelling, Analysis and Simulations for New Applications; Value: 87,500.00 GBP

01-Jan-2020 - 06-Jan-2025

Langer, Matthias (Principal Investigator) Waurick, Marcus (Co-investigator) Doherty, Michael (Research Co-investigator)

01-Jan-2018 - 01-Jan-2024

Langer, Matthias (Principal Investigator) Estrada, Ernesto (Co-investigator) Ross, Grant Jamieson (Research Co-investigator)

01-Jan-2015 - 19-Jan-2025

Langer, Matthias (Principal Investigator)

Block operator matrices are matrices whose entries are operators in Hilbert or Banach spaces. Such operators appear in a natural way when systems of differential equations with different order and type are investigated or an operator in a given space is considered that has a natural decomposition intosubspaces. In many applications of mathematical physics it is natural and fruitful to use the theory of block operator matrices. It is the aim to study spectral properties of such block operator matrices: location of the essential spectrum, variational principles and estimates for eigenvalues, investigation of spectral subspaces, basis properties of components of eigenvectors and generalised Fourier transforms. Particular emphasis is placed on unbounded block operator matrices, for which different cases have to be considered separately; these cases depend on the places where the strongest operators are located. The results should be applied to concrete operators arising in applications, mainly ordinary or partial differential operators.

01-Jan-2007 - 30-Jan-2009