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On the (sub)logarithmic property of the pole-, zero- and algebraic multiplicity of operator functions

Published online by Cambridge University Press:  20 January 2009

G. Philip A. Thijsse
G. Philip A. Thijsse
Affiliation:
Abt. Mathematik-Lehrstuhl IUniversität DortmundPostfach 50 05 00 4600 Dortmund 50Fed. Rep. of Germany
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This paper contains an extension of a result obtained by H. Bart, M. A. Kaashoek and D. C. Lay in (2). These authors studied the reduced algebraic multiplicity RM(A; λ0) of a meromorphic operator function at a point λ0 ∈ C. They proved that under certain conditions this quantity has logarithmic behaviour, i.e.,

For more restricted cases such results had been proved by others, notably I. C. Gohberg and E. I. Sigal (see (4) and (5)). Here we shall prove that such a result also holds for a larger class of operator functions than the diagonable functions considered in (2).

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 2 , June 1980 , pp. 207 - 217
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

REFERENCES

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