New analytical and geometrical aspects of the algebraic multiplicity

[摘要] This paper reveals some new analytical and geometrical properties of the generalized algebraic multiplicity, chi, introduced in [7,5] and further developed in [15,17,18]. In particular, it establishes a completely new connection between chi and the concept of local intersection index of algebraic varieties, a central device in Algebraic Geometry. This link between Nonlinear Spectral Theory and Algebraic Geometry provides to chi with a deep geometrical meaning. Moreover, chi is characterized through the new notion of local determinant of the Schur operator associated to the linear path, 2(lambda). (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-01

[关键词] Intersection index;Local determinant;Algebraic multiplicity