Comparison of powers of differential polynomials

H. G. Ghazaryan

Eurasian mathematical journal, Tome 14 (2023) no. 4, pp. 23-46.

Résumé

Necessary and sufficient conditions are obtained for a polynomial $P$ to be more powerful then a polynomial $Q$. These conditions are formulated in terms of the orders of generalized-homogeneous sub-polynomials, corresponding to these polynomials, and the multiplicity of their zeros. Applying these results, conditions are obtained, under which a monomial ${\xi }^v$ for a certain set of multi-indices $v\in {\mathfrak{R}}^{\ast }$ can be estimated via terms of a given degenerate polynomial $P$.

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