The diverging and converging components of localized wave solutions are studied within the framework of both the Whittaker and Weyl plane wave expansions. The specific example of the splash pulse is considered because its evanescent components could be derived in an explicit closed form. It is shown that, in the Weyl picture, the evanescent fields associated with the diverging and converging co...

We propose a very general construction of simple Virasoro modules generalizing and including both highest weight and Whittaker modules. This reduces the problem of classification of simple Virasoro modules which are locally finite over a positive part to classification of simple modules over a family of finite dimensional solvable Lie algebras. For one of these algebras all simple modules are c...

We construct families of irreducible representations for a class of quantum groups Uq(fm(K,H). First, we realize these quantum groups as Hyperbolic algebras. Such a realization yields natural families of irreducible weight representations for Uq(fm(K,H)). Second, we study the relationship between Uq(fm(K,H)) and Uq(fm(K)). As a result, any finite dimensional weight representation of Uq(fm(K,H))...

The relation between the quantum defects, μλ, and scattering phases, δλ, in the single-channel Quantum Defect Theory (QDT) is discussed with an emphasis on their analyticity properties for both integer and noninteger values of the orbital angular momentum parameter λ. To derive an accurate relation between μλ and δλ for asymptotically-Coulomb potentials, the QDT is formally developed for the Wh...