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math.CA2026
Walsh Analysis in the Twenty-First Century: Convergence, Summability, Nonlinear Approximation, Universality, and Digital Applications
Sergo A. Episkoposian
Walsh analysis connects ordered Fourier convergence, summability, nonlinear approximation, and universal representation through a common character algebra. This survey examines dev…
math.CA2026
Diagonal and branchwise criteria for universal Fourier series
Sergo A. Episkoposian
We characterize diagonal profiles admitting universal real trigonometric Fourier series with factors in and , , $1\le…
math.FA2026
Compactness and Spectral Properties of Multiplier Operators in the Walsh System
Michael Ruzhansky, Sergo A. Episkoposian, Rafik Yeghoyan
We investigate compactness and spectral properties of multiplier operators associated with the Walsh system in the spaces , . Building upon previously establi…