10 papers
Weyl Quantization of Exponential Lie Groups for Square Integrable Representations
Stine Marie Berge, Simon Halvdansson
We construct a general quantization procedure for square integrable functions on well-behaved connected exponential Lie groups. The Lie groups in question should admit at least one…
A Quantum Harmonic Analysis Approach to Segal Algebras
Eirik Berge, Stine Marie Berge, Robert Fulsche
In this article, we study a commutative Banach algebra structure on the space , where the denotes the trace class operator…
Yang-Mills connections and sigma-models on quantum Heisenberg manifolds
Stine Marie Berge, Sooran Kang, Franz Luef
We construct a spectral triple on a quantum Heisenberg manifold, which generalizes the results of Chakraborty and Shinha, and associate to it an energy functional on the set of pro…
Eigenvalues on Spherically Symmetric Manifolds
Stine Marie Berge
In this article we will explore Dirichlet Laplace eigenvalues on balls on spherically symmetric manifolds. We will compare any Dirichlet Laplace eigenvalue with the corresponding D…
Kuttler-Sigillito's Inequalities and Rellich-Christianson Identity
Stine Marie Berge
This article has two main objectives. The first one is to show Kuttler-Sigillito's type inequalities involving the mixed Neumann-Dirichlet, mixed Steklov-Dirichlet, and mixed Robin…
Affine Quantum Harmonic Analysis
Eirik Berge, Stine M. Berge, Franz Luef +1
We develop a quantum harmonic analysis framework for the affine group. This encapsulates several examples in the literature such as affine localization operators, covariant integra…
On the three ball theorem for solutions of the Helmholtz equation
Stine Marie Berge, Eugenia Malinnikova
Let be a solution of the Helmholtz equation with the wave number , , on a small ball in either , , or . For a fix…
The Affine Wigner Distribution
Eirik Berge, Stine Marie Berge, Franz Luef
We examine the affine Wigner distribution from a quantization perspective with an emphasis on the underlying group structure. One of our main results expresses the scalogram as (af…
Convexity Properties of Harmonic Functions on Parameterized Families of Hypersurfaces
Stine Marie Berge
It is known that the -norms of a harmonic function over spheres satisfies some convexity inequality strongly linked to the Almgren's frequency function. We examine the $L^{2…
A Lichnerowicz estimate for the spectral gap of the sub-Laplacian
Stine Marie Berge, Erlend Grong
For a second order operator on a compact manifold satisfying the strong Hörmander condition, we give a bound for the spectral gap analogous to the Lichnerowicz estimate for the Lap…