This is a question about terminology. Is there any common name for the trivial extension of a real function $f \colon \mathbb{R} \to \mathbb{R}$ to several variables $\tilde{f} \colon \mathbb{R}^n \to \mathbb{R}^n$?
By "trivial extension", I mean defining $\tilde{f}$ in terms of $f$ as $\tilde{f}(x_1, \dots, x_n) = (f(x_1), \dots, f(x_n))$.
As a simple example, if we have a trigonometric function like $sin(x)$, we can trivially extend it to $\mathbb{R}^3$ as $\sin(x, y, z) = (\sin(x), \sin(y), \sin(z))$. I'm just wondering if there is any accepted name and well-known reference for this simple way of building multivariate functions.
I don't think there is a generally accepted and generally understood term here. You might say $\tilde f$ is the $k$-fold tensor product of itself in some space $\bigotimes_1^k V$ of multivariate functions, or use some notation like $f^\otimes$, but you would also have to explain precisely what you mean to the audience. Which would end up taking more words and notation than simply giving the formula directly.