Harmonic Analysis and Qualitative Uncertainty Principle

This paper investigates the mathematical nature of qualitative uncertainty principle (QUP), which plays an important role in mathematics, physics and engineering fields. Consider a 3-tuple (K, H1, H2) that K: H1→H2 is an integral operator. Suppose a signal f H1, Ω1 and Ω2 are domains on which f, Kf define respectively. Does this signal f vanish if |Σ(f)|<|Ω1|and|Σ(Kf)|<|Ω2|? The excesses and deficiencies of integral kernel K(ω, t) are found to be greatly related to this general formulation of QUP. The complete point theory of integral kernel is established to