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Analytic functional

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An element of the space , the dual of the space of analytic functions defined on an open subset of , i.e. a functional on . Thus, a distribution with compact support is an analytic functional. There exists a compact set , said to be the support of the analytic functional , on which is concentrated: For any open set the functional can be extended to so that for all the following inequality is valid:

where is a constant depending on . There exists a measure with support in such that

An analytic functional is defined in a similar manner on a space of real-valued functions.


Comments

For applications to partial differential equations, see [a1].

References

[a1] L. Ehrenpreis, "Fourier analysis in several complex variables" , Wiley (Interscience) (1970)
[a2] L. Hörmander, "An introduction to complex analysis in several variables" , North-Holland (1973) pp. Sect. 4.5
How to Cite This Entry:
Analytic functional. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Analytic_functional&oldid=13936
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article