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CHARACTERIZATION OF POLYNOMIALS

V. E. SÁNDOR SZABÓ

Department of Analysis, Institute of Mathematics, Budapest University of Technology and Economics, Műegyetem rkp. 3-9., H-1111, Budapest, Hungary

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https://doi.org/10.1142/S0219530513500152Cited by:0 (Source: Crossref)

Abstract

In 1954, it was proved that if f is infinitely differentiable in the interval I and some derivatives (of order depending on x) vanish at each x, then f is a polynomial. Later, it was generalized for the multivariable case. A further extension for distributions is possible. If Ω ⊆ Rⁿ is a non-empty connected open set, and for every , there exists m(φ) ∈ N such that (D^αu)(φ) = 0 for all multi-indices α satisfying ‖α‖ = m(φ), then u is a polynomial (in distributional sense).

Keywords:

AMSC: 35D99, 46F05

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