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On some questions for the q-integration operator

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Abstract

We use the q-Duhamel product to provide a Banach algebra structure to some closed subspaces of the Wiener disk- algebra \(W_{+}\left( \mathbb {D}\right) \) of analytic functions on the unit disk \(\mathbb {D}\) of the complex plane \(\mathbb {C.}\) We study the q-integration operator on \(W_{+}\left( \mathbb {D}\right) ,\) namely, we characterize invariant subspaces of this operator and describe its extended eigenvalues and extended eigenvectors. Moreover, we prove an addition formula for the spectral multiplicity of the direct sum of q-integration operator on \(W_{+}\left( \mathbb {D}\right) \) and some Banach space operator.

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Acknowledgements

The author thanks the referees for their useful remarks and suggestions which improved the presentation of the paper. I also would like to thank the Deanship of Scientific Research, the College of Sciences Research Center for their support.

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  1. Mubariz T. Garayev

    Present address: Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

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  1. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, B. Vagabzade Str. 9, Baku, 370141, Azerbaijan

    Mubariz T. Garayev

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Correspondence to Mubariz T. Garayev.

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Garayev, M.T. On some questions for the q-integration operator. Acta Sci. Math. (Szeged) 89, 183–200 (2023). https://doi.org/10.1007/s44146-023-00064-z

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