Preprint No.
A-99-14
Ehrhard Behrends, Olga Katkova, Anna Vishnyakova
A note on $l^p$-norms
Abstract: Let $x_{1},\l,x_{n}$ and $y_{1},\l,y_{n}$ be
nonnegative numbers. If the $l^p$-norm of $(x_{1},\l,x_{n})$
coincides with that of $(y_{1},\l,y_{n})$ for $n$ different values of
$p>0$, then the $x_{i}$ are a permutation of the $y_{i}$.
This generalizes a well-known algebraic result which concerns
the exponents $p=1,\l,n$.
Some consequences as well as some generalizations to infinite
sequences and to functions are also discussed.
Keywords: $l^p$-norm, Dirichlet series, sign change, M\"untz-Szasz theorem.
Mathematics Subject Classification (MSC91): 46B25 Classical Banach spaces in the general theory
Language: ENG
Available: Pr-A-99-14.ps
Contact: Behrends,Ehrhard; Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (behrends@math.fu-berlin.de)
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