@phdthesis{Wallenta2015,
  author    = {Wallenta, Daniel},
  title     = {Sequences of compact curvature},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-87489},
  school      = {Universit{\"a}t Potsdam},
  pages     = {viii, 73},
  year      = {2015},
  abstract  = {By perturbing the differential of a (cochain-)complex by "small" operators, one obtains what is referred to as quasicomplexes, i.e. a sequence whose curvature is not equal to zero in general. In this situation the cohomology is no longer defined. Note that it depends on the structure of the underlying spaces whether or not an operator is "small." This leads to a magical mix of perturbation and regularisation theory. In the general setting of Hilbert spaces compact operators are "small." In order to develop this theory, many elements of diverse mathematical disciplines, such as functional analysis, differential geometry, partial differential equation, homological algebra and topology have to be combined. All essential basics are summarised in the first chapter of this thesis. This contains classical elements of index theory, such as Fredholm operators, elliptic pseudodifferential operators and characteristic classes. Moreover we study the de Rham complex and introduce Sobolev spaces of arbitrary order as well as the concept of operator ideals. In the second chapter, the abstract theory of (Fredholm) quasicomplexes of Hilbert spaces will be developed. From the very beginning we will consider quasicomplexes with curvature in an ideal class. We introduce the Euler characteristic, the cone of a quasiendomorphism and the Lefschetz number. In particular, we generalise Euler's identity, which will allow us to develop the Lefschetz theory on nonseparable Hilbert spaces. Finally, in the third chapter the abstract theory will be applied to elliptic quasicomplexes with pseudodifferential operators of arbitrary order. We will show that the Atiyah-Singer index formula holds true for those objects and, as an example, we will compute the Euler characteristic of the connection quasicomplex. In addition to this we introduce geometric quasiendomorphisms and prove a generalisation of the Lefschetz fixed point theorem of Atiyah and Bott.},
  language  = {en}
}
@phdthesis{DiGesu2012,
  author    = {Di Ges{\`u}, Giacomo},
  title     = {Semiclassical spectral analysis of discrete Witten Laplacians},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-65286},
  school      = {Universit{\"a}t Potsdam},
  year      = {2012},
  abstract  = {A discrete analogue of the Witten Laplacian on the n-dimensional integer lattice is considered. After rescaling of the operator and the lattice size we analyze the tunnel effect between different wells, providing sharp asymptotics of the low-lying spectrum. Our proof, inspired by work of B. Helffer, M. Klein and F. Nier in continuous setting, is based on the construction of a discrete Witten complex and a semiclassical analysis of the corresponding discrete Witten Laplacian on 1-forms. The result can be reformulated in terms of metastable Markov processes on the lattice.},
  language  = {en}
}
@phdthesis{Hohberger2006,
  author    = {Hohberger, Horst},
  title     = {Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-11574},
  school      = {Universit{\"a}t Potsdam},
  year      = {2006},
  abstract  = {We consider scattering in \$\R^n\$, \$n\ge 2\$, described by the Schr\"odinger operator \$P(h)=-h^2\Delta+V\$, where \$V\$ is a short-range potential. With the aid of Maslov theory, we give a geometrical formula for the semiclassical asymptotics as \$h\to 0\$ of the scattering amplitude \$f(\omega_-,\omega_+;\lambda,h)\$ \$\omega_+\neq\omega_-\$) which remains valid in the presence of focal points at infinity (caustics). Crucial for this analysis are precise estimates on the asymptotics of the classical phase trajectories and the relationship between caustics in euclidean phase space and caustics at infinity.},
  subject      = {Mathematik},
  language  = {en}
}
@article{SukiasyanMelkonyan2020,
  author    = {Sukiasyan, Hayk and Melkonyan, Tatev},
  title     = {Semi-recursive algorithm of piecewise linear approximation of two-dimensional function by the method of worst segment dividing},
  series = {Lectures in pure and applied mathematics},
  journal   = {Lectures in pure and applied mathematics},
  number    = {6},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-485-2},
  issn      = {2199-4951},
  doi       = {10.25932/publishup-47198},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471982},
  pages     = {35 -- 44},
  year      = {2020},
  language  = {en}
}
@unpublished{KiselevTarkhanov2012,
  author    = {Kiselev, Oleg M. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Scattering of autoresonance trajectories upon a separatrix},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56880},
  year      = {2012},
  abstract  = {We study asymptotic properties of solutions to the primary resonance equation with large amplitude on a long time interval.},
  language  = {en}
}
@unpublished{Tarkhanov2005,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Root functions of elliptic boundary problems in domains with conic points of the boundary},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29812},
  year      = {2005},
  abstract  = {We prove the completeness of the system of eigen and associated functions (i.e., root functions) of an elliptic boundary value problem in a domain whose boundary is a smooth surface away from a finite number of points, each of them possesses a neighbourhood where the boundary is a conical surface.},
  language  = {en}
}
@unpublished{BoeckmannBieleNeuberetal.1997,
  author    = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland and Niebsch, Jenny},
  title     = {Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14360},
  year      = {1997},
  abstract  = {The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.},
  language  = {en}
}
@unpublished{KleinZitt2008,
  author    = {Klein, Markus and Zitt, Pierre-Andr{\´e}},
  title     = {Resonances for a diffusion with small noise},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49448},
  year      = {2008},
  abstract  = {We study resonances for the generator of a diffusion with small noise in R(d) : L = -∈∆ + ∇F * ∇, when the potential F grows slowly at infinity (typically as a square root of the norm). The case when F grows fast is well known, and under suitable conditions one can show that there exists a family of exponentially small eigenvalues, related to the wells of F. We show that, for an F with a slow growth, the spectrum is R+, but we can find a family of resonances whose real parts behave as the eigenvalues of the "quick growth" case, and whose imaginary parts are small.},
  language  = {en}
}
@unpublished{GilKrainerMendoza2004,
  author    = {Gil, Juan B. and Krainer, Thomas and Mendoza, Gerardo A.},
  title     = {Resolvents of elliptic cone operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26820},
  year      = {2004},
  abstract  = {We prove the existence of sectors of minimal growth for general closed extensions of elliptic cone operators under natural ellipticity conditions. This is achieved by the construction of a suitable parametrix and reduction to the boundary. Special attention is devoted to the clarification of the analytic structure of the resolvent.},
  language  = {en}
}
@unpublished{Krainer2005,
  author    = {Krainer, Thomas},
  title     = {Resolvents of elliptic boundary problems on conic manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29773},
  year      = {2005},
  abstract  = {We prove the existence of sectors of minimal growth for realizations of boundary value problems on conic manifolds under natural ellipticity conditions. Special attention is devoted to the clarification of the analytic structure of the resolvent.},
  language  = {en}
}