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On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem

Abdullah Mir (2023)

Czechoslovak Mathematical Journal

We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend some classical results from complex to the quaternionic setting as well.

On weighted Hardy spaces on the unit disk

Evgeny A. Poletsky, Khim R. Shrestha (2015)

Banach Center Publications

In this paper we completely characterize those weighted Hardy spaces that are Poletsky-Stessin Hardy spaces H u p . We also provide a reduction of H problems to H u p problems and demonstrate how such a reduction can be used to make shortcuts in the proofs of the interpolation theorem and corona problem.

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