Now showing items 1-7 of 7

• #### Geometric quantization of integrable systems with hyperbolic singularities ﻿

[OWP-2009-01] (Mathematisches Forschungsinstitut Oberwolfach, 2009)
We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. ...
• #### Heisenberg-Weyl algebra revisited: combinatorics of words and paths ﻿

[OWP-2009-02] (Mathematisches Forschungsinstitut Oberwolfach, 2009)
The Heisenberg–Weyl algebra, which underlies virtually all physical representations of Quantum Theory, is considered from the combinatorial point of view. We provide a concrete model of the algebra in terms of paths on a ...
• #### Minimal Riesz energy on the sphere for axis-supported external fields ﻿

[OWP-2009-04] (Mathematisches Forschungsinstitut Oberwolfach, 2009)
Abstract. We investigate the minimal Riesz $s$-energy problem for positive measures on the d-dimensional unit sphere $\mathbb{S}^d$ in the presence of an external field induced by a point charge, and more generally by ...
• #### On the Directionally Newton-non-degenerate Singularities of Complex Hypersurfaces ﻿

[OWP-2008-16] (Mathematisches Forschungsinstitut Oberwolfach, 2008)
We introduce a minimal generalization of Newton-non-degenerate singularities of hypersurfaces. Roughly speaking, an isolated hypersurface singularity is called directionally Newton-non-degenerate if the local embedded ...
• #### On the δ=const Collisions of Singularities of Complex Plane Curves ﻿

[OWP-2008-15] (Mathematisches Forschungsinstitut Oberwolfach, 2008)
We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or ...
• #### Urn Models & Operator Ordering Procedures ﻿

[OWP-2008-06] (Mathematisches Forschungsinstitut Oberwolfach, 2008-03-10)
Ordering of operators is purely combinatorial task involving a number of commutators shuffling components of operator expression to desired form. Here we show how it can be illustrated by simple urn models in which normal ...
• #### Weyl-Titchmarsh Functions of Vector-Valued Sturm-Liouville Operators on the Unit Interval ﻿

[OWP-2008-13] (Mathematisches Forschungsinstitut Oberwolfach, 2008)
The matrix-valued Weyl-Titchmarsh functions $M(\lambda)$ of vector-valued Sturm-Liouville operators on the unit interval with the Dirichlet boundary conditions are considered. The collection of the eigenvalues (i.e., poles ...