We detail a simple procedure (easily convertible to an algorithm) for constructing, from quasi-uniform samples of f, a sequence of linear spline functions converging to the monotone rearrangement of f, in the case where f is an almost everywhere continuous function defined on a bounded set Ω with negligible boundary. Under additional assumptions on f and Ω, we prove that the convergence of the sequence is uniform. We also show that the same procedure applies to arbitrary measurable functions too, but with the substantial difference that in this case the procedure has only a theoretical interest and cannot be converted to an algorithm.
Barbarino, G., Bianchi, D., Garoni, C. (2022). Constructive approach to the monotone rearrangement of functions. EXPOSITIONES MATHEMATICAE, 40(1), 155-175 [10.1016/j.exmath.2021.10.004].
Constructive approach to the monotone rearrangement of functions
Garoni Carlo
2022-01-01
Abstract
We detail a simple procedure (easily convertible to an algorithm) for constructing, from quasi-uniform samples of f, a sequence of linear spline functions converging to the monotone rearrangement of f, in the case where f is an almost everywhere continuous function defined on a bounded set Ω with negligible boundary. Under additional assumptions on f and Ω, we prove that the convergence of the sequence is uniform. We also show that the same procedure applies to arbitrary measurable functions too, but with the substantial difference that in this case the procedure has only a theoretical interest and cannot be converted to an algorithm.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
