Generalization of the Fourier Calculus and Wigner Function

In this paper, we consider -periodical functions and, which are defined on the curve given by the equation: |x|^P+|y|^P=1, p>1 on as functions of its length. Considering and as an independent functional system, we construct the theory similar to Fourier analysis with the proper weights. For these weights, we establish an analogous of the Riemannian theorem. The adjoint representations are introduced and dual theory is developed. These Fourier representations can be used for approximation of the oscillation processes.