Schrödinger networks and their Cartesian products | Zendy

Abodayeh K. | Zendy; Anandam V. | Zendy

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Schrödinger networks and their Cartesian products

Author(s) -

Abodayeh K.,

Anandam V.

Publication year - 2021

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.7034

Subject(s) - cartesian product , mathematics , cartesian coordinate system , markov chain , graph , product (mathematics) , schrödinger's cat , schrödinger equation , harmonic function , pure mathematics , mathematical analysis , discrete mathematics , geometry , statistics

A Schrödinger network is a suitable infinite graph on which certain potential‐theoretic aspects of the discrete Schrödinger equation can be studied. It is shown that the positive solutions of this discrete equation can be represented as integrals. The Cartesian product of Schrödinger networks, which has a bearing on Markov chains, is investigated. Also, we give a characterization of minimal positive harmonic functions on the the Cartesian product of Schrödinger networks.

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