Algebraic Multiplicity Through Logarithmic Residues
The stability results of Section 8.4 can be regarded as infinite-dimensional versions of the classic Rouché theorem. A closely related topic in complex function theory is the so-called argument principle, otherwise known as the logarithmic residue theorem, which has been established by Theorem 3.4.1 (for classical families) and Corollary 6.5.2 in a finite-dimensional setting.
KeywordsAsymptotic Expansion Open Neighborhood Operator Family Laurent Series Trace Operator
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