Szabó Sándor (BME): Characterization of polynomials
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Abstract:
In 1954 it was proved that if f  is infinitely differentiable in the
interval I  and some
derivative (of order depending on x) vanishes at each x, then f  is a
polynomial. Later it
was generalized for multivariable case. A further extension for
distributions is possible.
Our result implies the polynomial cases also.