For each prime p, a Vladimirov operator with positive exponent specifies p-adic diffusion equation and measure on the Skorokhod space of paths. The product, P, these measures fixed is probability product path spaces. adelic paths have full if only sum, σ, constants finite. Finiteness σ implies that there an operator, ΔA, associated whose fundamental solution gives rise to induced by P space. wi...

We show that any polynomial in the infinitesimal generators of a Lie group is essentially hypermaximal symmetric (and so has a spectral resolution), when suitably interpreted as an operator on a Hubert space, provided it is formally symmetric and commutes with all the infinitesimal generators. Such operators are frequently of use in investigations of the unitary representations of Lie groups. T...

We describe how to extend the notion of infinitesimal Markovian divisibility from quantum channels general linear maps and compact convex sets generators. give a approach toward proving necessary criteria for (infinitesimal) divisibility. With it, we prove two in any finite dimension d: an upper bound on determinant terms Θ(d)-power smallest singular value product Θ(d) values. These allow us an...

In this paper we consider superstring propagation in a nontrivial NS-NS background. We deform the world sheet stress tensor and supercurrent with an infinitesimal Bμν field. We construct the gauge-covariant super-Poincaré generators in this background and show that the Bμν field spontaneously breaks spacetime supersymmetry. We find that the gauge-covariant spacetime momenta cease to commute wit...

Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and obtain the corresponding algebras of generators. In this letter, we extend technique sparse representations arbitrary Lie algebras. We show that our method reproduces canonical (sparse) generators Lorentz group, as well U(n) SU(n) families groups. This approach is completely general c...

We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in C, n ≥ 1. For the case n = 1 we also completely describe the associated Koenigs function and we solve the embedding problem from a dynamical point of view, proving, among other things, that a generic semigroup of holomorphic self-maps of the unit disc is a semigroup of linear fractional...