Reciprocity for Fredholm operators (lefschetz numbers/steinberg symbols/holomorphic chains/local index)

R. W. Carey; J. D. Pincus

doi:10.1007/bf01204625

Reciprocity for Fredholm operators (lefschetz numbers/steinberg symbols/holomorphic chains/local index)

Integral Equations and Operator Theory ◽

10.1007/bf01204625 ◽

1986 ◽

Vol 9 (4) ◽

pp. 469-501 ◽

Cited By ~ 6

Author(s):

R. W. Carey ◽

J. D. Pincus

Keyword(s):

Fredholm Operators ◽

Local Index ◽

Lefschetz Numbers ◽

Holomorphic Chains

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On Local Index and the Cocycle Property for Lefschetz Numbers

Topics in Operator Theory and Interpolation ◽

10.1007/978-3-0348-9162-2_2 ◽

1988 ◽

pp. 45-86

Author(s):

R. W. Carey ◽

J. D. Pincus

Keyword(s):

Local Index ◽

Lefschetz Numbers ◽

Cocycle Property

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Heat kernel asymptotics, local index theorem and trace integrals for Cauchy-Riemann manifolds with S1 action

Mémoires de la Société mathématique de France ◽

10.24033/msmf.470 ◽

2019 ◽

Vol 162 ◽

pp. 1-140 ◽

Cited By ~ 1

Author(s):

Jin-Hsin Cheng ◽

Chin-Yu Hsiao ◽

I-Hsun Tsai

Keyword(s):

Heat Kernel ◽

Index Theorem ◽

Local Index ◽

Riemann Manifolds ◽

Heat Kernel Asymptotics ◽

Local Index Theorem ◽

Cauchy Riemann

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Global Perturbation of Nonlinear Eigenvalues

Advanced Nonlinear Studies ◽

10.1515/ans-2021-2127 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Julián López-Gómez ◽

Juan Carlos Sampedro

Keyword(s):

Perturbation Theory ◽

Spectral Parameter ◽

Classical Theory ◽

General Setting ◽

Perturbation Parameter ◽

Linear Operators ◽

Fredholm Operators ◽

Index Zero ◽

Finite Dimensional ◽

Nonlinear Eigenvalues

Abstract This paper generalizes the classical theory of perturbation of eigenvalues up to cover the most general setting where the operator surface 𝔏 : [ a , b ] × [ c , d ] → Φ 0 ⁢ ( U , V ) {\mathfrak{L}:[a,b]\times[c,d]\to\Phi_{0}(U,V)} , ( λ , μ ) ↦ 𝔏 ⁢ ( λ , μ ) {(\lambda,\mu)\mapsto\mathfrak{L}(\lambda,\mu)} , depends continuously on the perturbation parameter, μ, and holomorphically, as well as nonlinearly, on the spectral parameter, λ, where Φ 0 ⁢ ( U , V ) {\Phi_{0}(U,V)} stands for the set of Fredholm operators of index zero between U and V. The main result is a substantial extension of a classical finite-dimensional theorem of T. Kato (see [T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Class. Math., Springer, Berlin, 1995, Chapter 2, Section 5]).

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