Equivalent Riesz products on the unit sphere

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Specific conditions are sufficient to ensure the mutual absolute continuity of two standard or pluriharmonic Riesz products defined on the unit sphere of complex Euclidean space. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Evgueni Doubtsov

doi:10.1017/s0017089526101104

September 11, 2026Glasgow Mathematical Journal

Equivalent Riesz products on the unit sphere

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Key Points

Identify sufficient conditions for the mutual absolute continuity of standard or pluriharmonic Riesz products defined on the unit sphere of complex Euclidean space.
Applied harmonic analysis and measure theory techniques to evaluate infinite product measures on the complex Euclidean unit sphere.
Derived analytical conditions governing the convergence and mutual equivalence of standard and pluriharmonic Riesz product constructions.
Established sufficient criteria ensuring the mutual absolute continuity of two standard Riesz products on the complex unit sphere.
Extended these equivalence criteria to pluriharmonic Riesz product measures within the same multidimensional geometric setting.

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Abstract

We obtain conditions sufficient for the mutual absolute continuity of two standard or pluriharmonic Riesz products defined on the unit sphere of the complex Euclidean space.

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Evgueni Doubtsov (2026) studied this question.

synapsesocial.com/papers/6aa7b3060926e14a848b1b04 https://doi.org/10.1017/s0017089526101104

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Equivalent Riesz products on the unit sphere

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Equivalent Riesz products on the unit sphere

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