To study operator algebras with symmetries in a wide sense we introduce a notion of relative convolution operators induced by a Lie algebra. Relative convolutions recover many important classes of… Expand

Quantum-classical mixing is studied by a group-theoretical approach, and a quantum-classical equation of motion is derived. The quantum-classical bracket entering the equation preserves the Lie… Expand

This paper lays down a foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theory based on the representation theory of SL(2,R) group.… Expand

We study geometry of two-dimensional models of conformal space-time based on the group of Mobius transformation. The natural geometric invariants, called cycles, are used to linearize Mobius action.… Expand

Usually the only difference between relativistic quantization and standard one is that the Lagrangian of the system under consideration should be Lorentz invariant. The standard approaches are… Expand

We explore a function theory connected with the principal series representation of SL(2,R) in contrast to standard complex analysis connected with the discrete series.
We construct counterparts for… Expand