The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of constraints, a primary kinematical representation is derived in the form of a reproducing kernel and its associated reproducing kernel Hilbert space. Constra...

ll rights reserved. Recently the Chebyshev kernel has been proposed for SVM and it has been proven that it is a valid kernel for scalar valued inputs in [11]. However in pattern recognition, many applications require multidimensional vector inputs. Therefore there is a need to extend the previous work onto vector inputs. In [11], although it is not stated explicitly, the authors recommend evalu...