• 대한수학회논문집
• /
• 제37권2호
• /
• pp.409-414
• /
• 2022

Let A ∈ B(X) be a spectral operator on a non-archimedean Banach space over an algebraically closed field. In this note, we give a necessary and sufficient condition on the resolvent of A so that the discrete semigroup consisting of powers of A is uniformly-bounded.

• 대한수학회보
• /
• 제53권4호
• /
• pp.1185-1196
• /
• 2016

We show a class of homogeneous polynomials of Fermat-Waring type such that for a polynomial P of this class, if $P(f_1,{\ldots},f_{N+1})=P(g_1,{\ldots},g_{N+1})$, where $f_1,{\ldots},f_{N+1}$; $g_1,{\ldots},g_{N+1}$ are two families of linearly independent entire functions, then $f_i=cg_i$, $i=1,2,{\ldots},N+1$, where c is a root of unity. As a consequence, we prove that if X is a hypersurface defined by a homogeneous polynomial in this class, then X is a unique range set for linearly non-degenerate non-Archimedean holomorphic curves.

• 호남수학학술지
• /
• 제18권1호
• /
• pp.1-4
• /
• 1996

• 대한수학회논문집
• /
• 제37권1호
• /
• pp.65-74
• /
• 2022

A valued field (K, ν) is called defectless if each of its finite extensions is defectless. In [1], Aghigh and Khanduja posed a question on defectless extensions of henselian valued fields: "if every simple algebraic extension of a henselian valued field (K, ν) is defectless, then is it true that (K, ν) is defectless?" They gave an example to show that the answer is "no" in general. This paper explores when the answer to the mentioned question is affirmative. More precisely, for a henselian valued field (K, ν) such that each of its simple algebraic extensions is defectless, we investigate additional conditions under which (K, ν) is defectless.