The Road to Reality

Some more on hyperfunctions - sec. 9.7
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Author:  fallingup [ 16 Apr 2008, 02:17 ]
Post subject:  Some more on hyperfunctions - sec. 9.7

Roger Penrose says that according to the excision theorem the notion of a hyperfunction (f,g) is independent of the regions on which f and g are defined.
The excision theorem is an algebraic topology theorem that relates to cohomology groups on sheaves, or something like that. It is probably not very complicated at heart, but there's an "Introduction to the theory of hyperfunctions" by Hikosaburo Komatsu which has a more basic proof, using the Mittag-Leffler theorem in complex analysis. He uses a variant of the usual Mittag-Leffler theorem, explained in an obscure, dense (think London fog) book "An introduction to complex analysis in several variables" by Lars Hoermander.
Enjoy! Komatsu's explanation is quite lucid, almost light reading.

When Komatsu writes
(2.3) [F] = F(x+i0) - F(x-i0)
I think what he means by F(x+i0) is the limit that F approaches as you go towards x in the -i direction.

Author:  DimBulb [ 01 Jun 2009, 03:40 ]
Post subject:  Re: Some more on hyperfunctions - sec. 9.7

I don't get it. How do I see the attachment?

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