On the Generalisation of the Hahn-Jordan Decomposition for Real Càdlàg FunctionsReportar como inadecuado



 On the Generalisation of the Hahn-Jordan Decomposition for Real Càdlàg Functions


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For a real c\`{a}dl\`{a}g function f and a positive constant c we find another c\`{a}dl\`{a}g function, which has the smallest total variation pos- sible among all functions uniformly approximating f with accuracy c-2. The solution is expressed with the truncated variation, upward truncated variation and downward truncated variation introduced in L1 and L2. They are always finite even if the total variation of f is infinite, and they may be viewed as the generalisation of the Hahn-Jordan decomposition for real c\`{a}dl\`{a}g functions. We also present partial results for more general functions.



Autor: Rafał M. Łochowski

Fuente: https://archive.org/







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