Parseval's identity

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Parseval's identity

[′pär·sə·vəlz ī′den·əd·ē]
(mathematics)
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From this, by virtue of Parseval's equality for orthogonal bases, we have that
From this, by Parseval's equality, it is easy to obtain an estimate:
Since [absolute value of [epsilon]] < 1, from this, by Parseval's equality, we find
It details the elementary theory of infinite series; the basic properties of Taylor and Fourier series, series of functions, and the applications of uniform convergence; double series, changes in the order of summation, and summability; power series and real analytic functions; and additional topics in Fourier series, such as summability, Parseval's equality, and the convolution theorem.
Moreover, for each function f [member of] [L.sub.2](0,[infinity]) with a finite support, the following Parseval's equality holds:
In order to check if ([q.sub.M](x), [h.sub.M]) is sufficiently close to the desired pair, one can use Parseval's equality (2.3) for a sufficiently wide set of the test functions f.