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Maru Guadie

Publications and source records attributed to Maru Guadie.

2 recordsLinked to original sources
arXiv2013

Stability estimates for discrete harmonic functions on product domains

We study the Dirichlet problem for discrete harmonic functions in unbounded product domains on multidimensional lattices. First we prove some versions of the Phragmén-Lindelöf theorem and use Fourier series to obtain a discrete analog of the three-line theorem for the gradients of harmonic functions in a strip. Then we derive estimates for the discrete harmonic measure and use elementary spectral inequalities to obtain stability estimates for Dirichlet problem in cylinder domains.

math.AP↗
arXiv2013

A note on unique continuation for discrete harmonic functions

In this note we give a quantitative version of the following simple observation: a discrete harmonic function on the lattice may vanish at each point of a large cube without being zero identically, at the same time there is a version of three balls theorem for discrete harmonic functions since they resemble continuous ones on large scales.

math.AP↗