Erhard Aichinger,
"Local polynomial functions on the integers"
, in Rivista di Matematica della Universita di Parma, 1997, Erhard Aichinger: Local polynomial functions on the integers. Riv. Mat. Univ. Parma (5) 6, 169-177, 1997
Original Titel:
Local polynomial functions on the integers
Sprache des Titels:
Englisch
Englische Kurzfassung:
In 1977, H.\ Hule and W.\ N\"obauer started to investigate
those unary functions on an algebra that can be interpolated at
a fixed number of points by a polynomial function.
In the present note, we consider the special case where the
algebra is the ring of integers. For every natural number $n$,
we compute a characterization of those selfmaps on the integers that
can be interpolated at every subset with at most $n$ elements
by a polynomial function with integral coefficients.
By the results of H.\ Lausch and W.\ N\"obauer, we know that there are functions
(even uncountably many of them) that can be interpolated
by polynomial functions with integral coefficients at each
finite subset of their domain, but fail to be polynomial functions.
In this note we show that uncountably many of such
``almost polynomial'' functions exist for every countably
infinite integral domain.
Journal:
Rivista di Matematica della Universita di Parma
Erscheinungsjahr:
1997
Notiz zum Zitat:
Erhard Aichinger: Local polynomial functions on the integers. Riv. Mat. Univ. Parma (5) 6, 169-177, 1997
Anzahl der Seiten:
9
Reichweite:
international
Publikationstyp:
Aufsatz / Paper in sonstiger referierter Fachzeitschrift
Forschungs-