Publications of Matthias Langer

A list of articles and editorial work can be found below.

My publications can also be found on the following web pages:

Articles

[61] M. Langer and H. Woracek,
Karamata's theorem for regularised Cauchy transforms,
Proc. Roy. Soc. Edinburgh Sect. A, to appear
abstract    journal
[60] M. Langer, R. Pruckner and H. Woracek,
Estimates for the Weyl coefficient of a two-dimensional canonical system,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), to appear
abstract   
[59] M. Langer, R. Pruckner and H. Woracek,
Canonical systems whose Weyl coefficients have dominating real part,
J. Anal. Math. 152 (2024), 361–400
abstract    journal
[58] L. Kerr, W. Lamb and M. Langer,
Discrete fragmentation equations with time-dependent coefficients,
Discrete Contin. Dyn. Syst. Ser. S 17 (2024), 1947–1965
abstract    journal
[57] S. McLauchlan, Y. Han, M. Langer and A. Majumdar,
The radial hedgehog solution in the Landau–de Gennes theory: effects of the bulk potentials,
Phys. D 459 (2024), 134019, 16 pp.
abstract    journal
[56] M. Langer and H. Woracek,
Direct and inverse spectral theorems for a class of canonical systems with two singular endpoints,
in "Function Spaces, Theory and Applications",
Fields Institute Communications, vol. 87, Springer, Cham, 2023, pp. 105–205
abstract    article
[55] L. Kerr, W. Lamb and M. Langer,
Discrete fragmentation systems in weighted ℓ1 spaces,
J. Evol. Equ. 20 (2020), 1419–1451
abstract    journal
[54] J. Giribet, M. Langer, F. Martínez Pería, F. Philipp and C. Trunk,
Spectral enclosures for a class of block operator matrices,
J. Funct. Anal. 278 (2020), 108455, 30 pp.
abstract    journal
[53] E. Estrada, E. Hameed, M. Langer and A. Puchalska,
Path Laplacian operators and superdiffusive processes on graphs. II. Two-dimensional lattice,
Linear Algebra Appl. 555 (2018), 373–397
abstract    journal
[52] J. Behrndt, M. Langer, V. Lotoreichik and J. Rohleder,
Spectral enclosures for non-self-adjoint extensions of symmetric operators,
J. Funct. Anal. 275 (2018), 1808–1888
abstract    journal
[51] J. Giribet, M. Langer, L. Leben, A. Maestripieri, F. Martínez Pería and C. Trunk,
Spectrum of J-frame operators,
Opuscula Math. 38 (2018), 623–649
abstract    journal
[50] N. Cooper, E. Da Ros, J. Nute, D. Baldolini, P. Jouve, L. Hackermüller and M. Langer,
Collimated dual species oven source and its characterisation via spatially resolved fluorescence spectroscopy,
J. Phys. D 51 (2018), 105602, 8 pp.
abstract    journal
[49] J. Behrndt, M. Langer, V. Lotoreichik and J. Rohleder,
Quasi boundary triples and semibounded self-adjoint extensions,
Proc. Roy. Soc. Edinburgh Sect. A 147 (2017), 895–916
abstract    journal
[48] J. Behrndt, M. Langer and V. Lotoreichik,
Trace formulae for Schrödinger operators with singular interactions,
in "Functional Analysis and Operator Theory for Quantum Physics",
European Math. Soc., Zürich, 2017, pp. 129–152
abstract    link
[47] M. Langer and M. Strauss,
Spectral properties of unbounded J-self-adjoint block operator matrices,
J. Spectr. Theory 7 (2017), 137–190
abstract    journal
[46] E. Estrada, E. Hameed, N. Hatano and M. Langer,
Path Laplacian operators and superdiffusive processes on graphs. I.
One-dimensional case
,
Linear Algebra Appl. 523 (2017), 307–334
abstract    journal
[45] B. Jacob, M. Langer and C. Trunk,
Variational principles for self-adjoint operator functions arising from second order systems,
Oper. Matrices 10 (2016), 501–531
abstract    journal
[44] J. Behrndt, M. Langer and V. Lotoreichik,
Boundary triples for Schrödinger operators with singular interactions on hypersurfaces,
Nanosystems: Phys. Chem. Math. 7 (2016), 290–302
abstract    journal
[43] M. Langer and M. Strauss,
Triple variational principles for self-adjoint operator functions,
J. Funct. Anal. 270 (2016), 2019–2047
abstract    journal
[42] J. Behrndt, G. Grubb, M. Langer and V. Lotoreichik,
Spectral asymptotics for resolvent differences of elliptic operators with δ and δ'-interactions on hypersurfaces,
J. Spectr. Theory 5 (2015), 697–729
abstract    journal   
[41] B.R. Duffy, M. Langer and S.K. Wilson,
Closed-form solutions of a thermocapillary free-film problem due to Pukhnachev,
European J. Appl. Math. 26 (2015), 721–741
abstract    journal   
[40] M. Langer and H. Woracek,
Distributional representations of 𝒩κ(∞)-functions,
Math. Nachr. 288 (2015), 1127–1149
abstract    journal   
[39] M. Langer and H. Woracek,
Stability of N-extremal measures,
Methods Funct. Anal. Topology 21 (2015), 69–75
abstract    journal   
[38] K.M.M. Tant, A.J. Mulholland, M. Langer and A. Gachagan,
A fractional Fourier transform analysis of the scattering of ultrasonic waves,
Proc. R. Soc. Lond. Ser. A 471 (2015), 20140958, 14 pp.
abstract    journal   
[37] M. Langer and H. Woracek,
Stability of the derivative of a canonical product,
Complex Anal. Oper. Theory 8 (2014), 1183–1224
abstract    journal
[36] O.O. Ibrogimov, H. Langer, M. Langer and C. Tretter,
Essential spectrum of systems of singular differential equations,
Acta Sci. Math. (Szeged) 79 (2013), 423–465
abstract    journal
[35] J. Banasiak, W. Lamb and M. Langer,
Strong fragmentation and coagulation with power-law rates,
J. Engrg. Math. 82 (2013), 199–215
abstract    journal
[34] M. Langer and H. Woracek,
Indefinite Hamiltonian systems whose Titchmarsh–Weyl coefficients have no finite generalized poles of non-positive type,
Oper. Matrices 7 (2013), 477–555
abstract    journal
[33] J. Behrndt, M. Langer and V. Lotoreichik,
Trace formulae and singular values of resolvent power differences of self-adjoint elliptic operators,
J. London Math. Soc. (2) 88 (2013), 319–337
abstract    journal
[32] J. Behrndt, M. Langer and V. Lotoreichik,
Spectral estimates for resolvent differences of self-adjoint elliptic operators,
Integral Equations Operator Theory 77 (2013), 1–37
abstract    journal
[31] J. Behrndt, M. Langer and V. Lotoreichik,
Schrödinger operators with δ and δ'-potentials supported on hypersurfaces,
Ann. Henri Poincaré 14 (2013), 385–423
abstract    journal
[30] M. Langer and H. Woracek,
The exponential type of the fundamental solution of an indefinite Hamiltonian system,
Complex Anal. Oper. Theory 7 (2013), 285–312
abstract    journal
[29] B.M. Brown, H. Langer and M. Langer,
Bessel-type operators with an inner singularity,
Integral Equations Operator Theory 75 (2013), 257–300
abstract    journal
[28] J. Behrndt and M. Langer,
Elliptic operators, Dirichlet-to-Neumann maps and quasi boundary triples,
in "Operator Methods for Boundary Value Problems",
London Math. Soc. Lecture Note Series, vol. 404,
Cambridge University Press, Cambridge, 2012, pp. 121–160
abstract    book
[27] L. Smith, W. Lamb, M. Langer and A. McBride,
Discrete fragmentation with mass loss,
J. Evol. Equ. 12 (2012), 181–201
abstract    journal
[26] F.P. da Costa, M. Grinfeld, M. Langer, N.J. Mottram and J.T. Pinto,
Kickback in nematic liquid crystals,
Quart. Appl. Math. 70 (2012), 99–110
abstract    journal
[25] M. Grinfeld, M. Langer and N.J. Mottram,
Nematic viscosity estimation using director kickback dynamics,
Liquid Crystals 38 (2011), 981–987
abstract    journal
[24] M. Langer and H. Woracek,
A function space model for canonical systems with an inner singularity,
Acta Sci. Math. (Szeged) 77 (2011), 101–165
abstract    journal
[23] M. Langer and H. Woracek,
A local inverse spectral theorem for Hamiltonian systems,
Inverse Problems 27 (2011), 055002, 17pp.
abstract    journal
[22] J. Behrndt and M. Langer,
On the adjoint of a symmetric operator,
J. Lond. Math. Soc. (2) 82 (2010), 563–580
abstract    journal
[21] J. Behrndt, M. Langer, I. Lobanov, V. Lotoreichik and I.Yu. Popov,
A remark on Schatten–von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains,
J. Math. Anal. Appl. 371 (2010), 750–758
abstract    journal
[20] B.M. Brown, M. Langer, M. Marletta, C. Tretter and M. Wagenhofer,
Eigenvalue enclosures and exclosures for non-self-adjoint problems in hydrodynamics,
LMS J. Comput. Math. 13 (2010), 65–81
abstract    journal
[19] M. Langer and A. Luger,
On norms in indefinite product spaces,
Oper. Theory Adv. Appl. 198 (2010), 259–264
abstract    journal
[18] M. Langer and H. Woracek,
Dependence of the Weyl coefficient on singular interface conditions,
Proc. Edinburgh Math. Soc. (2) 52 (2009), 445–487
abstract    journal
[17] B.M. Brown, M. Langer and K.M. Schmidt,
The HELP inequality on trees,
Proc. Sympos. Pure Math. 77 (2008), 337–354
abstract    book
[16] H. Langer, M. Langer, A. Markus and C. Tretter,
The Virozub–Matsaev condition and spectrum of definite type for self-adjoint operator functions,
Complex Anal. Oper. Theory 2 (2008), 99–134
abstract    journal
[15] J. Behrndt and M. Langer,
Boundary value problems for elliptic partial differential operators on bounded domains,
J. Funct. Anal. 243 (2007), 536–565
abstract    journal
[14] M. Langer and C. Tretter,
Variational principles for eigenvalues of the Klein–Gordon equation,
J. Math. Phys. 47 (2006), 103506, 18 pp.
abstract    journal
[13] M. Langer,
A general HELP inequality connected with symmetric operators,
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 462 (2006), 587–606
abstract    journal
[12] M. Langer and A. Luger,
Scalar generalized Nevanlinna functions: realizations with block operator matrices,
Oper. Theory Adv. Appl. 162 (2006), 253–276
abstract    journal
[11] H. Langer, M. Langer, A. Markus and C. Tretter,
Spectrum of definite type of self-adjoint operators in Krein spaces,
Linear and Multilinear Algebra 53 (2005), 115–136
abstract    journal
[10] B.M. Brown, M. Langer and M. Marletta,
Spectral concentrations and resonances of a second order block operator matrix and an associated λ-rational Sturm–Liouville problem,
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 (2004), 3403–3420
abstract    journal
[9] M. Kraus, M. Langer and C. Tretter,
Variational principles and eigenvalue estimates for unbounded block operator matrices and applications,
J. Comput. Appl. Math. 171 (2004), 311–334
abstract    journal
[8] H. Langer, M. Langer and Z. Sasvári,
Continuations of Hermitian indefinite functions and corresponding canonical systems: an example,
Methods Funct. Anal. Topology 10 (2004), 39–53
abstract    journal
[7] D. Eschwé and M. Langer,
Variational principles for eigenvalues of self-adjoint operator functions,
Integral Equations Operator Theory 49 (2004), 287–321
abstract    journal
[6] B.M. Brown, M. Langer, M. Marletta, C. Tretter and M. Wagenhofer,
Eigenvalue bounds for the singular Sturm–Liouville problem with a complex potential,
J. Phys. A 36 (2003), 3773–3787
abstract    journal
[5] H. Langer, M. Langer and C. Tretter,
Variational principles for eigenvalues of block operator matrices,
Indiana Univ. Math. J. 51 (2002), 1427–1459
abstract    journal
[4] M. Langer and H. Woracek,
A characterization of intermediate Weyl coefficients,
Monatsh. Math. 135 (2002), 137–155
abstract    journal
[3] M. Langer,
Resonances of a λ-rational Sturm–Liouville problem,
Proc. Roy. Soc. Edinburgh Sect. A 131 (2001), 709–720
abstract    journal
[2] V. Adamjan, H. Langer and M. Langer,
A spectral theory for a λ-rational Sturm–Liouville problem,
J. Differential Equations 171 (2001), 315–345
abstract    journal
[1] M. Langer,
Eigenvalues of a λ-rational Sturm–Liouville problem,
Math. Nachr. 210 (2000), 163–176  
abstract    journal

Editorial work

[2] Indefinite Inner Product Spaces.
Section of the book “Operator Theory” in the SpringerReference series, Springer, 2015.
Edited by Matthias Langer and Harald Woracek.
link to book
[1] Operator Theory and Indefinite Inner Product Spaces.
Lectures presented on the occasion of the retirement of Heinz Langer in the
Colloquium on Operator Theory held at the Vienna University of Technology, Vienna, March 2004.
Edited by Matthias Langer, Annemarie Luger and Harald Woracek.
Operator Theory: Advances and Applications, vol. 163. Birkhäuser Verlag, Basel, 2006, xxxii+397pp.
link to book