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Properties and Applications
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 ofExpand
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Mixing Quantum and Classical Mechanics
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 LieExpand
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Elliptic, Parabolic and Hyperbolic Analytic Function Theory--0: Geometry of Domains
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
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Two-dimensional conformal models of space-time and their compactification
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
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Relativistic Quantization and Improved Equation for a Free Relativistic Particle
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 areExpand
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Analysis in $R^{1,1}$ or the Principal Function Theory
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 forExpand
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