What does this research mean for the field?

The convergence of Fejér means at ω-Walsh-Lebesgue points for Walsh-Fourier series generalizes to Vilenkin-Fejér means, θ-summations, matrix transforms, and Nörlund summations of multi-dimensional Vilenkin-Fourier series. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To generalize convergence results for multi-dimensional Walsh–Fourier series to Vilenkin–Fejér means and broader summability methods at generalized Lebesgue points.

September 2, 2026Journal of Geometric AnalysisOpen Access

Vilenkin–Lebesgue points and summations of bounded multi-dimensional Vilenkin–Fourier series

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Authors

MSMáté Szilveszter RTRodolfo Toledo FWFerenc Weisz

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Overview

Theoretical analysis demonstrates convergence of multi-dimensional Vilenkin–Fourier summations in integrable functions, expanding harmonic analysis across non-dyadic settings.

Key Points

To generalize convergence results for multi-dimensional Walsh–Fourier series to Vilenkin–Fejér means and broader summability methods at generalized Lebesgue points.
Formulated theoretical extensions of ω-Walsh–Lebesgue points to the Vilenkin group framework for d-dimensional integrable functions.
Analyzed convergence behaviors of Vilenkin–Fourier series as indices tend toward infinity within a cone.
Demonstrated that multi-dimensional Vilenkin–Fejér means converge to the function at each generalized Vilenkin–Lebesgue point when indices approach infinity restricted to a cone.
Established analogous convergence theorems for θ-summations, matrix transform methods, and Nörlund summations.

Cite This Study

Szilveszter et al. (2026) studied this question.

synapsesocial.com/papers/6a97e28dc562ede874ec6bcd https://doi.org/10.1007/s12220-026-02588-6

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September 2, 2026Journal of Geometric AnalysisOpen Access

Vilenkin–Lebesgue points and summations of bounded multi-dimensional Vilenkin–Fourier series

View Full Paper

Ask AI

Bookmark

Authors

MSMáté Szilveszter RTRodolfo Toledo FWFerenc Weisz

Discussion

Member takes

Overview

Theoretical analysis demonstrates convergence of multi-dimensional Vilenkin–Fourier summations in integrable functions, expanding harmonic analysis across non-dyadic settings.

Key Points

To generalize convergence results for multi-dimensional Walsh–Fourier series to Vilenkin–Fejér means and broader summability methods at generalized Lebesgue points.
Formulated theoretical extensions of ω-Walsh–Lebesgue points to the Vilenkin group framework for d-dimensional integrable functions.
Analyzed convergence behaviors of Vilenkin–Fourier series as indices tend toward infinity within a cone.
Demonstrated that multi-dimensional Vilenkin–Fejér means converge to the function at each generalized Vilenkin–Lebesgue point when indices approach infinity restricted to a cone.
Established analogous convergence theorems for θ-summations, matrix transform methods, and Nörlund summations.

Cite This Study

Szilveszter et al. (2026) studied this question.

synapsesocial.com/papers/6a97e28dc562ede874ec6bcd https://doi.org/10.1007/s12220-026-02588-6

Also Consider

Synapse has enriched one closely related paper. Consider it for comparative context:

1Almost everywhere convergence of two-dimensional Walsh-Nörlund means2024 · 2 citations

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