We consider the description of translation invariant subspaces of a weighted Hardy space in the half plane. The obtained result includes the Beurling–Lax theorem for the Hardy space as a special case. We discuss the problem of generalization of the definition of inner function.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 6, pp. 853–857, June, 2014.
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Dil’nyi, V.M. On Invariant Subspaces in Weighted Hardy Spaces. Ukr Math J 66, 955–960 (2014). https://doi.org/10.1007/s11253-014-0985-9
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DOI: https://doi.org/10.1007/s11253-014-0985-9