TY - JOUR
T1 - Generalized harmonic functions on trees
T2 - Universality and frequent universality
AU - Biehler, N.
AU - Nestoridi, E.
AU - Nestoridis, V.
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/11/1
Y1 - 2021/11/1
N2 - Recently, harmonic functions and frequently universal harmonic functions on a tree T have been studied, taking values on a separable Fréchet space E over the field C or R. In the present paper, we allow the functions to take values in a vector space E over a rather general field F. The metric of the separable topological vector space E is translation invariant and instead of harmonic functions we can also study more general functions defined by linear combinations with coefficients in F. We don't assume that E is complete and therefore we present an argument avoiding Baire's theorem.
AB - Recently, harmonic functions and frequently universal harmonic functions on a tree T have been studied, taking values on a separable Fréchet space E over the field C or R. In the present paper, we allow the functions to take values in a vector space E over a rather general field F. The metric of the separable topological vector space E is translation invariant and instead of harmonic functions we can also study more general functions defined by linear combinations with coefficients in F. We don't assume that E is complete and therefore we present an argument avoiding Baire's theorem.
KW - Boundary of the tree
KW - Frequent universality
KW - Topological and algebraic genericity
KW - Tree
KW - Universality
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U2 - 10.1016/j.jmaa.2021.125277
DO - 10.1016/j.jmaa.2021.125277
M3 - Article
AN - SCOPUS:85105517766
SN - 0022-247X
VL - 503
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
M1 - 125277
ER -