New analytical and geometrical aspects of the algebraic multiplicity

被引：2

作者：

Lopez-Gomez, Julian ^{[1
]}

Carlos Sampedro, Juan ^{[1
]}

机构：

[1] Univ Complutense Madrid, Inst Interdisciplinary Math IMI, Dept Anal & Appl Math, Madrid 28040, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 504卷 / 01期

关键词：

Intersection index; Local determinant; Algebraic multiplicity; LOCAL BIFURCATION-THEORY;

D O I：

10.1016/j.jmaa.2021.125375

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页数：21

共 26 条

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[2]

Bump Daniel., 1998, ALGEBRAIC GEOM

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