ABSTRACT
This chapter includes the study of some additional fundamental properties of the algebraic multiplicity constructed in Chapter 4. Among them, it will be shown that if https://www.w3.org/1998/Math/MathML"> L ( λ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429127830/f689fe4c-93e7-4d8b-873c-b9d56001164e/content/eq3022.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> is of class https://www.w3.org/1998/Math/MathML"> C ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429127830/f689fe4c-93e7-4d8b-873c-b9d56001164e/content/eq3023.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , Eq. 4.1 is satisfied, and there exists a local family of isomorphisms https://www.w3.org/1998/Math/MathML"> Φ ( λ ) : U → U https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429127830/f689fe4c-93e7-4d8b-873c-b9d56001164e/content/eq3024.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
