“Picone's Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Picone's Theorem

释义

Picone's Theorem

Let be integrable in , let be of bounded variation in , let denote the least upper boundof in , and let denote the total variation of in . Given the function

then the terms of its Legendre Series

where

is a Legendre Polynomial, satisfy the inequalities

for

(Sansone 1991).

See also Jackson's Theorem, Legendre Series

References

Picone, M. Appunti di Analise Superiore. Naples, Italy,, p. 260, 1940.

Sansone, G. Orthogonal Functions, rev. English ed. New York: Dover, pp. 203-205, 1991.

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