MathProblemsBank

19.3.2 Linear operators

Problem: Find all the values of the parameter \( \alpha>0 \), for which the operator \( T: L^{2}[0 ; 1] \rightarrow L^{2}[0 ; 1] \), \( (T f)(x)=x f(x)-f\left(x^{\alpha}\right) \) is continuous.