Chromatic series for functions of slow growth

Abstract

The theory of chromatic derivatives leads to chromatic series which replace Taylor's series for bandlimited functions. For such functions, these series have a global convergence property not shared by Taylor's series. In this work the theory is extended to bandlimited functions of slow growth. This includes many signals of practical importance such as polynomials, periodic functions and almost periodic functions. This extension also enables us to get improved local convergence results for chromatic series.

Keywords:

• orthogonal polynomials
• chromatic series
• Fourier transforms
• distributions

AMS Subject Classifications::

• 41A58
• 42A38
• 62E17
• 94A12