Abstract:

In this paper the authors give a definite meaning to any formal
trigonometrical series and generalize it to an abstract Hilbert space.
Then in the case L²(-∞,+∞) they discussed extensively the
 generalized expansion problem by Hermite functions, and applied to a
non-strictly nonlinear hyperbolic system.

Key words: Generalized expansion, Hilbert space, Hermite functions, hyperbolic system