Parseval theorem - integration in (-a, a)

[nirmal323]

Parseval's theorem !!!

Hello Everyone,
Is there relation of the Parseval's theorem with finite integration.
The Parsevals's theorem has the integration from (-∞, ∞).
I would like to know if there is any relation for integration from (-a, a) in the integration in the Parseval's theorem; where a is a real number.

Thank you.

 

[zorro]

Parseval's theorem !!!

Hi nirmal323,

In the case that one function has finite support (-a, a), then the integation in (-∞, ∞) reduces to integrate in (-a, a). But if the function has finite support in one domain, it doesn't have finite support in the other, so you should integrate in (-∞, ∞) in the other domain in order that Parseval's theorem holds.
Maybe an identity similar to Parseval's theorem but integrating over finite intervals is valid for Prolate spheroidal wave functions (of Landau and Pollak). I'm not sure now.
Regards

Z