C*-algebra of strong limit power functions

Motivated by problems in robust control of power signal set H₂ (e.g,, H₂ is not a vector space, Fourier analysis cannot be carried out on H₂ in general), we study those functions in H₂ which we call strong limit power. We show that the set of all such functions is a sufficiently large C^*-algebra. Fourier Analysis is carried out on the functions. In particular, the uniqueness of the Fourier expansion of a strong limit power function is established. Finally we point out how to analyze and reconstruct such functions.