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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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In this work we discuss “plank problems” for complex
Banach spaces and in particular for the classical Lp(µ) spaces. In
the case 1 ≤ p ≤ 2 we obtain optimal results and for finite dimensional
complex Banach spaces, in a special case, we have improved
an early result by K. Ball [3]. By using these results, in some cases
we are able to find best possible lower bounds for the norms of
homogeneous polynomials which are products of linear forms. In
particular, we give an estimate in the case of a real Hilbert space
which seems to be a difficult problem. We have also obtained some
results on the so-called n-th (linear) polarization constant of a Banach
space which is an isometric property of the space. Finally,
known polynomial inequalities have been derived as simple consequences
of various results related to plank problems.
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참고문헌 (29)
참고문헌 신청
/ / spaces math. proc.cambridge philos. soc.99 (1986)
/ 1923 / ¨Uber die Verteilung der Wurzeln bei gewissen algebraischen Gleichun-gen mit ganzahligen Koezienten 17
/ 1938 / Additions to the theory of polynomials in ormed linear spaces 44
/ 1951 / A solution of the plank problem 2
/ 1960 / An application of Jensen’s formula to polynomials 7 : 98100 ~
/ 1923 / ¨Uber die Verteilung der Wurzeln bei gewissen algebraischen Gleichun-gen mit ganzahligen Koezienten 17
/ 1938 / Additions to the theory of polynomials in ormed linear spaces 44
/ 1951 / A solution of the plank problem 2
/ 1960 / An application of Jensen’s formula to polynomials 7 : 98100 ~
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