A transformation from $e^{2\pi i nt}$ to $e^{2\pi i \lambda_nt}$

Question

Let $e_n:=e^{2\pi i nt}$, $f \in L^2[0,1]$ and $a_n=\langle f, e_n\rangle$. Then the expansion $f =\sum_{n\in\mathbb Z} a_n e_n$ is called the Fourier series representation of $f$, and $\left(\langle f, e_n\rangle \right)_{n\in\mathbb Z}$ is the sequence of Fourier coefficients of $f$. The Fourier coefficients are $$a_n=\int_0^1 f(t)\, e^{-2\pi i nt}dt\, , \quad n\in\mathbb Z\, .$$ I'm considering a transformation such that $$\mathcal T f:=\sum_{n\in\mathbb Z} \tilde a_n \tilde e_n\, , \quad \tilde a_n\neq a_n\, , \quad \tilde e_n=e^{2\pi i \lambda_nt}\quad \text{and} \quad \lambda_n\in\mathbb R\, .$$ The study of perturbed exponential system is not new but I was wondering if $\mathcal T$ is a particular kind of operator or transformation, already known in literature.