Discrete Potential Theory on Schrödinger Products

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DOI: https://doi.org/10.28924/2291-8639-24-2026-327
Published: Oct 5, 2026
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P. Swarnambigai, N. Nathiya, Discrete Potential Theory on Schrödinger Products, Int. J. Anal. Appl., 24 (2026), 327.

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P. Swarnambigai, N. Nathiya

Abstract

This article develops a discrete potential-theoretic framework for Cartesian products of infinite Schrödinger networks. We introduce the notion of product Schrödinger networks and define separately \(q\)-supermean and separately \(q\)-potential functions, establishing their structural and comparison properties. Integral representation theorems and a Riesz-type decomposition are proved for non-negative separately \(q\)-supermean functions on product networks. Furthermore, we present a classification of product Schrödinger networks based on bounded and unbounded mean behavior, showing how the \(q\)-mean (\(q\)-harmonic) and potential-theoretic nature of the product network are determined by the corresponding properties of the individual factor networks.

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