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Home » Issues » Archive of Issues » 2021 - 4 issue » pp. 640-650

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India Chennai
Year
2021
Volume
31
Issue
4
Pages
640-650
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Section Mathematics
Title Infinite Schrödinger networks
Author(-s) Nathiya N.a, Amulya Smyrna C.a
Affiliations Vellore Institute of Technology Chennaia
Abstract Finite-difference models of partial differential equations such as Laplace or Poisson equations lead to a finite network. A discretized equation on an unbounded plane or space results in an infinite network. In an infinite network, Schrödinger operator (perturbed Laplace operator, $q$-Laplace) is defined to develop a discrete potential theory which has a model in the Schrödinger equation in the Euclidean spaces. The relation between Laplace operator $\Delta$-theory and the $\Delta_q$-theory is investigated. In the $\Delta_q$-theory the Poisson equation is solved if the network is a tree and a canonical representation for non-negative $q$-superharmonic functions is obtained in general case.
Keywords $q$-harmonic functions, $q$-superharmonic functions, Schrödinger network, hyperbolic Schrödinger network, parabolic Schrödinger network, integral representation
UDC 517
MSC 31C20, 31A05, 31A10
DOI 10.35634/vm210408
Received 7 May 2021
Language English
Citation Nathiya N., Amulya Smyrna C. Infinite Schrödinger networks, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 4, pp. 640-650.
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