@article{HarutyunyanSchulze2006,
  author    = {Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The Zaremba problem with singular interfaces as a corner boundary value problem},
  series = {Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis},
  volume    = {25},
  journal   = {Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0926-2601},
  doi       = {10.1007/s11118-006-9020-6},
  pages     = {327 -- 369},
  year      = {2006},
  abstract  = {We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y, i.e., Au = f in int X, T (+/-) u = g(+/-) on int Y+/-, where Y is subdivided into subsets Y+/- with an interface Z and boundary conditions T+/- on Y+/- that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z subset of Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in Bull. Sci. Math. ( to appear). With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions.},
  language  = {en}
}
@phdthesis{Harutyunyan2018,
  author    = {Harutyunyan, Gohar},
  title     = {Spectroscopy at the limit},
  pages     = {X, 112},
  year      = {2018},
  language  = {en}
}
@article{FladHarutyunyanSchulze2015,
  author    = {Flad, Heinz-J{\"u}rgen and Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Singular analysis and coupled cluster theory},
  series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  volume    = {17},
  journal   = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  number    = {47},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c5cp01183c},
  pages     = {31530 -- 31541},
  year      = {2015},
  abstract  = {The primary motivation for systematic bases in first principles electronic structure simulations is to derive physical and chemical properties of molecules and solids with predetermined accuracy. This requires a detailed understanding of the asymptotic behaviour of many-particle Coulomb systems near coalescence points of particles. Singular analysis provides a convenient framework to study the asymptotic behaviour of wavefunctions near these singularities. In the present work, we want to introduce the mathematical framework of singular analysis and discuss a novel asymptotic parametrix construction for Hamiltonians of many-particle Coulomb systems. This corresponds to the construction of an approximate inverse of a Hamiltonian operator with remainder given by a so-called Green operator. The Green operator encodes essential asymptotic information and we present as our main result an explicit asymptotic formula for this operator. First applications to many-particle models in quantum chemistry are presented in order to demonstrate the feasibility of our approach. The focus is on the asymptotic behaviour of ladder diagrams, which provide the dominant contribution to short-range correlation in coupled cluster theory. Furthermore, we discuss possible consequences of our asymptotic analysis with respect to adaptive wavelet approximation.},
  language  = {en}
}
@article{FladHarutyunyanSchneideretal.2011,
  author    = {Flad, Heinz-J{\"u}rgen and Harutyunyan, Gohar and Schneider, Reinhold and Schulze, Bert-Wolfgang},
  title     = {Explicit Green operators for quantum mechanical Hamiltonians},
  series = {Manuscripta mathematica},
  volume    = {135},
  journal   = {Manuscripta mathematica},
  number    = {3-4},
  publisher = {Springer},
  address   = {New York},
  issn      = {0025-2611},
  doi       = {10.1007/s00229-011-0429-x},
  pages     = {497 -- 519},
  year      = {2011},
  abstract  = {We study a new approach to determine the asymptotic behaviour of quantum many-particle systems near coalescence points of particles which interact via singular Coulomb potentials. This problem is of fundamental interest in electronic structure theory in order to establish accurate and efficient models for numerical simulations. Within our approach, coalescence points of particles are treated as embedded geometric singularities in the configuration space of electrons. Based on a general singular pseudo-differential calculus, we provide a recursive scheme for the calculation of the parametrix and corresponding Green operator of a nonrelativistic Hamiltonian. In our singular calculus, the Green operator encodes all the asymptotic information of the eigenfunctions. Explicit calculations and an asymptotic representation for the Green operator of the hydrogen atom and isoelectronic ions are presented.},
  language  = {en}
}
@article{FladFladHarutyunyanSchulze2018,
  author    = {Flad, Heinz-J{\"u}rgen and Flad-Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Ellipticity of the quantum mechanical Hamiltonians},
  series = {Journal of pseudo-differential operators and applications},
  volume    = {9},
  journal   = {Journal of pseudo-differential operators and applications},
  number    = {3},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1662-9981},
  doi       = {10.1007/s11868-017-0201-4},
  pages     = {451 -- 467},
  year      = {2018},
  abstract  = {In paper (Flad and Harutyunyan in Discrete Contin Dyn Syst 420-429, 2011) is shown that the Hamiltonian of the helium atom in the Born-Oppenheimer approximation, in the case if two particles coincide, is an edge-degenerate operator, which is elliptic in the corresponding edge calculus. The aim of this paper is an analogous investigation in the case if all three particles coincide. More precisely, we show that the Hamiltonian in the mentioned case is a corner-degenerate operator, which is elliptic as an operator in the corner analysis.},
  language  = {en}
}
@article{FladFladHarutyunyanSchulze2020,
  author    = {Flad, Heinz-J{\"u}rgen and Flad-Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Explicit Green operators for quantum mechanical Hamiltonians},
  series = {Asian-European journal of mathematics : AEJM},
  volume    = {13},
  journal   = {Asian-European journal of mathematics : AEJM},
  number    = {7},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {1793-5571},
  doi       = {10.1142/S1793557120501223},
  pages     = {64},
  year      = {2020},
  abstract  = {We extend our approach of asymptotic parametrix construction for Hamiltonian operators from conical to edge-type singularities which is applicable to coalescence points of two particles of the helium atom and related two electron systems including the hydrogen molecule. Up to second-order, we have calculated the symbols of an asymptotic parametrix of the nonrelativistic Hamiltonian of the helium atom within the Born-Oppenheimer approximation and provide explicit formulas for the corresponding Green operators which encode the asymptotic behavior of the eigenfunctions near an edge.},
  language  = {en}
}
@article{FladHarutyunyanSchulze2016,
  author    = {Flad, H. -J. and Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Asymptotic parametrices of elliptic edge operators},
  series = {Journal of pseudo-differential operators and applications},
  volume    = {7},
  journal   = {Journal of pseudo-differential operators and applications},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1662-9981},
  doi       = {10.1007/s11868-016-0159-7},
  pages     = {321 -- 363},
  year      = {2016},
  abstract  = {We study operators on singular manifolds, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. We introduce asymptotic parametrices, using tools from cone and edge pseudo-differential algebras. Our structures are motivated by models of many-particle physics with singular Coulomb potentials that contribute higher order singularities in Euclidean space, determined by the number of particles.},
  language  = {en}
}