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

单词

Schwarz's Inequality

释义

Schwarz's Inequality

(1)

Written out explicitly

(2)

with equality Iff

with

a constant. To derive, let

be aComplex function and

a Complex constant such that

for some

and

. Since

(3)

with equality when

. Set

(4)

so that

(5)

Plugging (5) and (4) into (3) then gives


	(6)

(7)

(8)

(9)

Bessel's Inequality can be derived from this.
References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 11, 1972.

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 527-529, 1985.

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