I am reading “Signal processing for communications” by Paolo Prandoni and Martin Vetterli. In the section 4.4 The DTFT (Discrete-Time Fourier Transform) (p. 72 of 2008 ed.) they write:
The somewhat odd notation $X (e ^{j \omega}) $ is quite standard in the signal processing literature and offers several advantages: <...> regardless of context, it immediately identifies a function as the Fourier transform of a discrete-time sequence: for example $U(e^{j \lambda})$ is just as readily recognizable ...
My question: what $U(e^{j \lambda})$ is?
Because I can’t “readily recognize” it. And authors don't use it anywhere else in the text.
I suspect, that it is a common notation in English, related to complex numbers in general. But I had education in different language and didn’t have enough exposure to math in English. Or I simply don’t know. And, unfortunately, it is hard to create a relevant google search.
What they mean is just that $U(e^{j\lambda})$ is recognizable as a DTFT of some sequence $u[n]$, no matter what names one chooses for the function and for the frequency variable. I agree that they could have made their point a bit clearer.