Related papers: Regularization of the Kepler problem on the Sphere
The goal of the paper is to develop a method that will combine the use of variational techniques with regularization methods in order to study existence and multiplicity results for the periodic and the Dirichlet problem associated to the…
In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propose a regularization method to compute the inverse Laplace…
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…
It is shown that Euclidean field theory with polynomial interaction, can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered with…
We prove new results on existence of solutions for the prescribed gaussian curvature problem on the euclidean sphere S^2. Those results are achieved by relating this problem with the holomorphic triples theory on Riemann surfaces. We think…
We study periodic orbits in the spatial rotating Kepler problem from a symplectic-topological perspective. Our first main result provides a complete classification of these orbits via a natural parametrization of the space of Kepler orbits,…
We introduce the regularization Levi-Civita parameter for the `curved Kepler', i.e., motion under the `Kepler-Coulomb' potential in a configuration space with any constant curvature and metric of any signature type. Consistent use of this…
The $\mathcal{KS}$ map is revisited in terms of an $S^1$-action in $T^*\mathbb{H}_0$ with the bilinear function as the associated momentum map. Indeed, the $\mathcal{KS}$ transformation maps the $S^1$-fibers related to the mentioned action…
We develop a new regularization method for the stress-energy tensor and the two-point function of free quantum scalar fields propagating in cosmological spacetimes. We proceed by extending the adiabatic regularization scheme with the…
We study the Maslov correction to semiclassical states by using a K\"ahler regularized BKS pairing map from the energy representation to the Schr\"odinger representation. For general semiclassical states, the existence of this…
The spatial Kepler problem with a perturbation satisfying the rotational symmetry w.r.t. the $z$-axis and the reflection symmetry w.r.t. the $(x, y)$-plane, can be reduced to an Hamiltonian system with 2 degrees of freedom after fixing the…
In a series of papers, we investigate the reformulation of Epstein-Glaser renormalization in coordinate space, both in analytic and Hopf algebraic terms. This first article deals with analytical aspects. Some of the historically good…
We consider regularization methods based on the coupling of Tikhonov regularization and projection strategies. From the resulting constraint regularization method we obtain level set methods in a straight forward way. Moreover, we show that…
We consider the matrix regularization of fields on a Riemann surface which couple to gauge fields with a nonvanishing magnetic flux. We show that such fields are described as rectangular matrices in the matrix regularization. We construct…
This paper details the geometry of the Kustaanheimo-Stiefel mapping, which regularizes the Hamiltonian of the Kepler problem. It leans heavily on the work of J.-C. van der Meer.
We study the regularized $(2n-1)$-Kepler problem and other Hamiltonian systems which are related to the nilpotent coadjoint orbits of $U(n,n)$. The Kustaanheimo-Stiefel and Cayley regularization procedures are discussed and their…
We extend an implicit regularization scheme to be applicable in the $n$-dimensional space-time. Within this scheme divergences involving parity violating objects can be consistently treated without recoursing to dimensional continuation.…
It has been proposed that the noncommutative geometry of the "fuzzy" 2-sphere provides a nonperturbative regularization of scalar field theories. This generalizes to compact Kaehler manifolds where simple field theories are regularized by…
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…
We introduce an elliptic regularization of the PDE system representing the isometric immersion of a surface in $\mathbb R^{3}$. The regularization is geometric, and has a natural variational interpretation.