The consequences for Berezin’s quantization on symmetric spaces of the identity of the set of coherent vectors orthogonal to a fixed one with the cut locus are stated precisely. It is shown that functions expressing the coherent states, the covariant symbols of operators, the diastasis function, the characteristic and twopoint functions are defined when one variable does not belong to the cut l...

Applying the methods developed in [3], in [4] we have constructed generalized CS attached to the Jacobi group G1 = H1 oSU(1, 1), based on the homogeneous Kähler manifold D 1 = H1/R × SU(1, 1)/U(1) = C 1 × D1. Here D1 denotes the unit disk D1 = {w ∈ C ; |w| < 1}, and Hn is the (2n + 1)-dimensional real Heisenberg-Weyl group with Lie algebra hn. In [4] we have also emphasized that, when expressed...

First a set of coherent statesá la Klauder is formally constructed for the Coulomb problem in a curved space of constant positive curvature. Then the flat-space limit is taken to reduce the set for the radial Coulomb problem to a set of hydrogen atom coherent states corresponding to both the discrete and the continuous portions of the spectrum for a fixed ℓ sector.

In this note we prove that the derived categories of an abelian fibration and its dual are derived equivalent if and only if there is fiberwise equivalence. We also study the problem for K3−fibrations.

For use in calculating higher-order coherentand squeezedstate quantities, we derive generalized generating functions for the Hermite polynomials. They are given by ∑∞ n=0 z Hjn+k(x)/(jn + k)!, for arbitrary integers j ≥ 1 and k ≥ 0. Along the way, the sums with the Hermite polynomials replaced by unity are also obtained. We also evaluate the action of the operators exp[a(d/dx)] on well-behaved ...

Let ”Sn•n denote a sequence of polynomials orthogonal with respect to the Sobolev inner product f; g‘S = ∫ f x‘gx‘dψ0x‘ + λ ∫ f x‘gx‘dψ1x‘; where λ > 0 and ”dψ0; dψ1• is a so-called coherent pair with at least one of the measures dψ0 or dψ1 a Laguerre measure. We investigate the asymptotic behaviour of Snx‘ outside the supports of dψ0 and dψ1, and n→+∞. © 2000 Academic Press

This report summarizes typical laser systems now available for atmospheric probing. Experiments comparing coherent and incoherent receiving techniques are described and typical performance data presented.

Coherent sets of almost desirable gambles and credal sets are known to be equivalent models. That is, there exists a bijection between the two collections of sets preserving the usual operations, e.g. conditioning. Such a correspondence is based on the polarity theory for closed convex cones. Learning from this simple observation, in this paper we introduce a new (lexicographic) polarity theory...