@misc{Schrohe1998,
  author    = {Schrohe, Elmar},
  title     = {Wloka, J. T. [u.a.], Boundary value problems for eliptic systems},
  year      = {1998},
  language  = {en}
}
@misc{Boelling1995,
  author    = {B{\"o}lling, Reinhard},
  title     = {Tuschmann, W., Hawig, P., Sofia Kowalewskaja, ein Leben f{\"u}r Mathematik und Emanzipation; Basel [u.a.], Birkh{\"a}user, 1993},
  year      = {1995},
  language  = {de}
}
@misc{KleinRosenberger2018,
  author    = {Klein, Markus and Rosenberger, Elke},
  title     = {The tunneling effect for a class of difference operators},
  series = {Reviews in Mathematical Physics},
  volume    = {30},
  journal   = {Reviews in Mathematical Physics},
  number    = {4},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0129-055X},
  doi       = {10.1142/S0129055X18300029},
  pages     = {42},
  year      = {2018},
  abstract  = {We analyze a general class of self-adjoint difference operators H-epsilon = T-epsilon + V-epsilon on l(2)((epsilon Z)(d)), where V-epsilon is a multi-well potential and v(epsilon) is a small parameter. We give a coherent review of our results on tunneling up to new sharp results on the level of complete asymptotic expansions (see [30-35]). Our emphasis is on general ideas and strategy, possibly of interest for a broader range of readers, and less on detailed mathematical proofs. The wells are decoupled by introducing certain Dirichlet operators on regions containing only one potential well. Then the eigenvalue problem for the Hamiltonian H-epsilon is treated as a small perturbation of these comparison problems. After constructing a Finslerian distance d induced by H-epsilon, we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by this distance to the well. It follows with microlocal techniques that the first n eigenvalues of H-epsilon converge to the first n eigenvalues of the direct sum of harmonic oscillators on R-d located at several wells. In a neighborhood of one well, we construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low-lying eigenvalues of H-epsilon. These are obtained from eigenfunctions or quasimodes for the operator H-epsilon acting on L-2(R-d), via restriction to the lattice (epsilon Z)(d). Tunneling is then described by a certain interaction matrix, similar to the analysis for the Schrodinger operator (see [22]), the remainder is exponentially small and roughly quadratic compared with the interaction matrix. We give weighted l(2)-estimates for the difference of eigenfunctions of Dirichlet-operators in neighborhoods of the different wells and the associated WKB-expansions at the wells. In the last step, we derive full asymptotic expansions for interactions between two "wells" (minima) of the potential energy, in particular for the discrete tunneling effect. Here we essentially use analysis on phase space, complexified in the momentum variable. These results are as sharp as the classical results for the Schrodinger operator in [22].},
  language  = {en}
}
@misc{Schrohe1995,
  author    = {Schrohe, Elmar},
  title     = {Schulze, B.-W., Pseudo-Differential Boundary Value Problems, Conical Singularities, and Asymptotics; Berlin, Akademie-Verl., 1995},
  year      = {1995},
  language  = {en}
}
@misc{vanLeeuwenKunschNergeretal.2019,
  author    = {van Leeuwen, Peter Jan and Kunsch, Hans R. and Nerger, Lars and Potthast, Roland and Reich, Sebastian},
  title     = {Particle filters for high-dimensional geoscience applications: A review},
  series = {Quarterly journal of the Royal Meteorological Society},
  volume    = {145},
  journal   = {Quarterly journal of the Royal Meteorological Society},
  number    = {723},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0035-9009},
  doi       = {10.1002/qj.3551},
  pages     = {2335 -- 2365},
  year      = {2019},
  abstract  = {Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, including the geosciences, but their application to high-dimensional geoscience systems has been limited due to their inefficiency in high-dimensional systems in standard settings. However, huge progress has been made, and this limitation is disappearing fast due to recent developments in proposal densities, the use of ideas from (optimal) transportation, the use of localization and intelligent adaptive resampling strategies. Furthermore, powerful hybrids between particle filters and ensemble Kalman filters and variational methods have been developed. We present a state-of-the-art discussion of present efforts of developing particle filters for high-dimensional nonlinear geoscience state-estimation problems, with an emphasis on atmospheric and oceanic applications, including many new ideas, derivations and unifications, highlighting hidden connections, including pseudo-code, and generating a valuable tool and guide for the community. Initial experiments show that particle filters can be competitive with present-day methods for numerical weather prediction, suggesting that they will become mainstream soon.},
  language  = {en}
}
@misc{Boelling1998,
  author    = {B{\"o}lling, Reinhard},
  title     = {Neuenschwander, E., Riemanns Einf{\"u}hrung in die Funktionentheorie, eine quellenkritische Edition seiner Vorlesungen mit einer Bibliographie zur Wirkungsgeschichte der Riemannschen Funktionentheorie; G{\"o}ttingen, Vandenhoeck und Ruprecht, 1996},
  issn      = {0036-6978},
  year      = {1998},
  language  = {de}
}
@misc{Boelling1997,
  author    = {B{\"o}lling, Reinhard},
  title     = {Mathematics of the 19th century, geometry, analytic function theory / ed. by A. N. Kolmogorov ... ;Basel [u.a.], Birkh{\"a}user, 1996},
  issn      = {0036-6978},
  year      = {1997},
  language  = {en}
}
@misc{Schrohe1998,
  author    = {Schrohe, Elmar},
  title     = {Lesch, M., Operators of Fuchs type, conical singularities, and asymptotic methods},
  year      = {1998},
  language  = {en}
}
@misc{Schrohe1999,
  author    = {Schrohe, Elmar},
  title     = {Lesch, M., Operators of Fuchs type, conical singularities, and asymptotic methods},
  year      = {1999},
  language  = {en}
}
@misc{Schmidt1998,
  author    = {Schmidt, Hans-J{\"u}rgen},
  title     = {Karsinski, A., Inhomogeneous cosmological models; Cambridge, Univ. Press, 1997},
  year      = {1998},
  language  = {en}
}
@misc{Boelling1997,
  author    = {B{\"o}lling, Reinhard},
  title     = {Guzevic, D., Petr Petrovic Bazen, 1786 - 1838; Sankt-Peterburg, Nauka, 1995},
  year      = {1997},
  language  = {fr}
}
@misc{ShlapunovTarkhanov2017,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Golusin-Krylov formulas in complex analysis},
  series = {Complex variables and elliptic equations},
  volume    = {63},
  journal   = {Complex variables and elliptic equations},
  number    = {7-8},
  publisher = {Routledge},
  address   = {Abingdon},
  issn      = {1747-6933},
  doi       = {10.1080/17476933.2017.1395872},
  pages     = {1142 -- 1167},
  year      = {2017},
  abstract  = {This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.},
  language  = {en}
}
@misc{Jahnke1998,
  author    = {Jahnke, Thomas},
  title     = {F{\"u}hrer, L., P{\"a}dagogik des Mathematikunterrichts, eine Einf{\"u}hrung in die Fachdidaktik; Braunschweig, Vieweg, 1997},
  year      = {1998},
  language  = {de}
}
@misc{BeckerSchenkelSzabo2017,
  author    = {Becker, Christian and Schenkel, Alexander and Szabo, Richard J.},
  title     = {Differential cohomology and locally covariant quantum field theory},
  series = {Reviews in Mathematical Physics},
  volume    = {29},
  journal   = {Reviews in Mathematical Physics},
  number    = {1},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0129-055X},
  doi       = {10.1142/S0129055X17500039},
  pages     = {42},
  year      = {2017},
  abstract  = {We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C∗-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fr{\´e}chet-Lie group structure on differential cohomology groups.},
  language  = {en}
}
@misc{Lledo1999,
  author    = {Lled{\´o}, Fernando},
  title     = {Contributions to operator theory in spaces with an indefinite metric, the Heinz Langer anniversary volume, A. S. Dijksma ... eds.; Basel [u.a.], Birkh{\"a}user, 1998, ISBN 3-7643-6003-8},
  year      = {1999},
  language  = {en}
}
@misc{Schmidt1999,
  author    = {Schmidt, Hans-J{\"u}rgen},
  title     = {Cercignani, C., Scaling limits and models in physical process; Basel, Birkh{\"a}user, 1998},
  year      = {1999},
  language  = {en}
}