A Larger Class of Time-shift Invariant Localized Over-complete Eigenfunction System Which Contains Wavelets and Coherent States
Fuminori Sakaguchi · International Symposium on Information Theory and its Applications · 1994
A general mathematical formulation of a larger class of time-shift-invariant over-complete systems which are the eigenfunction systems of a class of operators is proposed. This class contains an over-complete wavelet system and the coherent state system as spacial cases. It is shown that there are many other over-complete eigenfunction systems than the two, where the time-shift of the wavepacket function is performed simply by the shift of the real part of the eigenvalue. Moreover, we propose an application of these eigenfunction systems to the pseudo-diagonalization problem of the autocorrelation functions of stochastic processes.