Bilinear integral form
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
The double integral
$$ J ( \phi , \psi ) = \int\limits _ { a } ^ { b } \int\limits _ { a } ^ { b } K(x, s) \phi (x) \overline{ {\psi (s) }}\; dx ds , $$
where $ K(x, s) $ is a given (usually complex-valued) square-integrable function of real variables, and $ \phi (x) $, $ \psi (x) $ are arbitrary (also complex-valued) square-integrable functions, while $ \overline{ {\psi (s) }}\; $ is the complex conjugate function of $ \psi (s) $. If $ \psi (s) = \phi (s) $, $ J( \phi , \phi ) $ is said to be a quadratic integral form.
How to Cite This Entry:
Bilinear integral form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bilinear_integral_form&oldid=46060
Bilinear integral form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bilinear_integral_form&oldid=46060
This article was adapted from an original article by B.V. Khvedelidze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article