If is Square Integrable over the Real axis, then any one of
the following implies the other two:
- 1. The Fourier Transform of is 0 for .
- 2. Replacing by , the function is analytic in the Complex Plane for and
approaches almost everywhere as . Furthermore,
for some number and
(i.e., the integral is bounded).
- 3. The Real and Imaginary Parts of are Hilbert
Transforms of each other.
© 1996-9 Eric W. Weisstein
1999-05-26