On the irreducibility of the generalized Laguerre polynomials
M. Filaseta, T.-Y. Lam (2002)
Acta Arithmetica
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M. Filaseta, T.-Y. Lam (2002)
Acta Arithmetica
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A partial answer is given to a problem of Ulas (2011), asking when the nth Stern polynomial is reciprocal.
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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.