Shouldn't it be \(\hat{\Phi}\)?

Missing full stop: "Approximation. We"

I assume the "=" shouldn't be there?

Shouldn't it be "Tikhonov" instead of "Thikonov"?

Little Typo: continous \(\to\) continuous

How is \(\Phi(u)\) definied?

Shouldn't it be just F instead of \(F_i\)?

Maybe the variable shouldn't named i since the imaginary number i is also concluded in the formula...

The spaces in the definition are a little bit confusing: If \(\mathcal{F}: L^1(\mathbb{R}^n;\mathbb{C}) \to C_0(\mathbb{R}^n;\mathbb{C})\) shouldn't we write \(\mathcal{F}^{-1}: C_0(\mathbb{R}^n;\mathbb{C}) \to L^1(\mathbb{R}^n;\mathbb{C})\) and \(\hat{f} \in C_0(\mathbb{R}^n;\mathbb{C})\)?

Using the given formula of definition 2.1 shouldn't we get $$\hat{H}{\Theta} = \frac{H{\Theta} - 75}{225 - 75} \cdot (250 - 0) + 0$$? (To be specific: 225 instead of 125 and 250 instead of 225?)

Sentence is written twice.

In the script version on StuOn the "S" of Somtimes is missing.

Assuming I understood the definition correctly, it is also possible to write: \(f : \Omega \to X \subset \mathbb{R}^m\), since f maps from Ω to \(\mathbb{R}^m\) and \(f \in X\) (isn't it)?