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On the diagonalization of holomorphic matrix functions of several variables

✍ Scribed by Dieter Heunemann

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
203 KB
Volume
95
Category
Article
ISSN
0025-584X

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✦ Synopsis

On the diagonalization of holomorphic matrix functions of several variables

By DIETER HETTNEMANN in Berlin (Eingegangen am 10.7. 1979)

Let X c C n be a domain of holomorphy, L(Ck) be the space of complex k x kmatrices and GL(Ck) be the group of the invertible complex k x k-matrices.

Two holomorphic matrix functions S: X -L(Ck) and T: X -L(Ck) are called locally holomorphically equivalent on X if for each point zEX there exist a neighborhood U of z and holomorphic invertible matrix functions M : U -GL(Ck) and

N : U -GL(Ck) such that

.MSN=T on U .

We call S and T globally holomorphically equivalent on X if there are global holomorphic invertible functions M : X -GL(Ck) and N : X -QL(Ck) such that H S N = T on X .

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