Re: Symmetries reflect unilaterality and vice versa

In article <erki6h$545$1@xxxxxxxxxxxxxxxx>, Eckard Blumschein
<blumschein@xxxxxxxxxxxxxxxxxxx> wrote:

Fourier transform of a unilateral function f(x), e.g. f(x)= 0 for x<0,
yields a complex-valued F(y) with symmetrical real part and
antisymmetrical imaginary part. Also vice versa. For physical
implications cf.
http://iesk.et.uni-magdeburg.de/~blumsche/M283.html
Is there any word that aptly denotes a pair of two values which just
differ in sign: positive or negative? What about a bivalent value?

If f is real-valued, and F is its Fourier transform, then F(-y) is the
complex conjugate of F(y). Equivalently, the real part of F is even,
and the imaginary part is odd.

Am I using the term "Fourier transform" in the same way as you? I
assume something like this:

F(y) = \integral_{-\infinity}^{+\infinity} f(x) e^{ixy} dx.

Chris Henrich

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