DSpace Collection:https://dspace.lboro.ac.uk/2134/24842015-04-02T00:19:30Z2015-04-02T00:19:30ZAnalysis of Schrodinger operators with inverse square potentials I: regularity results in 3DHunsicker, EugenieLi, HengguangNistor, VictorUski, Villehttps://dspace.lboro.ac.uk/2134/171712015-04-01T11:32:00Z2012-01-01T00:00:00ZTitle: Analysis of Schrodinger operators with inverse square potentials I: regularity results in 3D
Authors: Hunsicker, Eugenie; Li, Hengguang; Nistor, Victor; Uski, Ville
Abstract: Let V be a potential on R3 that is smooth everywhere except at a discrete set
S of points, where it has singularities of the form Z/ 2, with (x) = |x − p| for x close to p
and Z continuous on R3 with Z(p) > −1/4 for p 2 S. Also assume that and Z are smooth
outside S and Z is smooth in polar coordinates around each singular point. We either assume
that V is periodic or that the set S is finite and V extends to a smooth function on the radial
compactification of R3 that is bounded outside a compact set containing S. In the periodic
case, we let be the periodicity lattice and define T := R3/ . We obtain regularity results in
weighted Sobolev space for the eigenfunctions of the Schr¨odinger-type operator H = − + V
acting on L2(T), as well as for the induced k–Hamiltonians Hk obtained by restricting the
action of H to Bloch waves. Under some additional assumptions, we extend these regularity
and solvability results to the non-periodic case. We sketch some applications to approximation
of eigenfunctions and eigenvalues that will be studied in more detail in a second paper.
Description: This article is closed access.2012-01-01T00:00:00ZScattering theory of the p-form Laplacian on manifolds with generalized cuspsHunsicker, EugenieRoidos, NikolaosStrohmaier, Alexanderhttps://dspace.lboro.ac.uk/2134/171682015-04-01T10:47:00Z2014-01-01T00:00:00ZTitle: Scattering theory of the p-form Laplacian on manifolds with generalized cusps
Authors: Hunsicker, Eugenie; Roidos, Nikolaos; Strohmaier, Alexander
Abstract: In this paper we consider scattering theory on manifolds with special cusp-like metric singularities of warped product type g=dx 2 +x −2a h , where a>0 . These metrics form a natural subset in the class of metrics with warped product singularities and they can be thought of as interpolating between hyperbolic and cylindrical metrics. We prove that the resolvent of the Laplace operator acting on p -forms on such a manifold extends to a meromorphic function defined on the logarithmic cover of the complex plane with values in the bounded operators between weighted L 2 -spaces. This allows for a construction of generalized eigenforms for the Laplace operator as well as for a meromorphic continuation of the scattering matrix. We give a precise description of the asymptotic expansion of generalized eigenforms on the cusp and find that the scattering matrix satisfies a functional equation.
Description: This article is closed access.2014-01-01T00:00:00ZA parametrix construction for the Laplacian on Q-rank 1 locally symmetric spaceHunsicker, Eugeniehttps://dspace.lboro.ac.uk/2134/171672015-03-31T15:39:58Z2014-01-01T00:00:00ZTitle: A parametrix construction for the Laplacian on Q-rank 1 locally symmetric space
Authors: Hunsicker, Eugenie
Editors: Ruzhansky, M.; Turunen, V.
Abstract: This paper presents the construction of parametrices for the Gauss-Bonnet and
Hodge Laplace operators on noncompact manifolds modelled on Q-rank 1 locally symmetric
spaces. These operators are, up to a scalar factor, -di erential operators, that is, they live
in the generalised -calculus studied by the authors in a previous paper, which extends work
of Melrose and Mazzeo. However, because they are not totally elliptic elements in this calculus,
it is not possible to construct parametrices for these operators within the -calculus. We
construct parametrices for them in this paper using a combination of the b-pseudodi erential
operator calculus of R. Melrose and the -pseudodi erential operator calculus. The construction
simpli es and generalizes the construction done by Vaillant in his thesis for the Dirac
operator. In addition, we study the mapping properties of these operators and determine the
appropriate Hlibert spaces between which the Gauss-Bonnet and Hodge Laplace operators are
Fredholm. Finally, we establish regularity results for elements of the kernels of these operators.
Description: This conference paper is closed access.2014-01-01T00:00:00ZImproving statistical skills through students’ participation in the development of resourcesBiza, IreneVande Hey, Eugeniehttps://dspace.lboro.ac.uk/2134/171662015-03-31T10:49:57Z2015-01-01T00:00:00ZTitle: Improving statistical skills through students’ participation in the development of resources
Authors: Biza, Irene; Vande Hey, Eugenie
Abstract: This paper summarizes the evaluation of a project that involved undergraduate mathematics students in the development of teaching and learning resources for statistics modules taught in various departments of a university. This evaluation regards students’ participation in the project and its impact on their learning of statistics, as characterized in terms of statistical reasoning, statistical thinking, and skills for statistical consultancy. The participation of students is evaluated from the viewpoint of communities of practice. The evaluation resulted in a characterization of the benefits of such a project and suggestions for implementations of future projects, and in addition brought to light new theoretical elements both as regards the learning of statistics and as regards communities of practice. In particular, the analysis highlighted contributions of the students involved to resource development practice in the community of university statistics teachers, as well as contributions to students’ learning as a result of participation in this community.
Description: This paper is embargoed until October 2015.2015-01-01T00:00:00Z