Displaying similar documents to “On a certain functional equation in the algebra of polynomials with complex coefficients.”

On stable polynomials

Miloslav Nekvinda (1989)

Aplikace matematiky

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The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.

Local polynomials are polynomials

C. Fong, G. Lumer, E. Nordgren, H. Radjavi, P. Rosenthal (1995)

Studia Mathematica

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We prove that a function f is a polynomial if G◦f is a polynomial for every bounded linear functional G. We also show that an operator-valued function is a polynomial if it is locally a polynomial.