INFINITE SCHRODINGER NETWORKS

被引：4

作者：

Nathiya, N. ^{[1
]}

Smyrna, C. Amulya ^{[1
]}

机构：

[1] Vellore Inst Technol Chennai, Div Math, Sch Adv Sci, Chennai 600127, Tamil Nadu, India

来源：

VESTNIK UDMURTSKOGO UNIVERSITETA-MATEMATIKA MEKHANIKA KOMPYUTERNYE NAUKI | 2021年 / 31卷 / 04期

关键词：

q-harmonic functions; q-superharmonic functions; Schrodinger network; hyperbolic Schrodinger network; parabolic Schrodinger network; integral representation; UNIQUENESS; OPERATORS;

D O I：

10.35634/vm210408

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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, Schrodinger operator (perturbed Laplace operator, q-Laplace) is defined to develop a discrete potential theory which has a model in the Schrodinger 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.

引用

页码：640 / 650

页数：11

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