The Callias Index Formula Revisited

These lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and rel...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Gesztesy, Fritz (Autor), Waurick, Marcus (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2016.
Edición:1st ed. 2016.
Colección:Lecture Notes in Mathematics, 2157
Temas:
Differential equations.
Operator theory.
Functional analysis.
Differential Equations.
Operator Theory.
Functional Analysis.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Introduction.-Notational Conventions
  • Functional Analytic
  • On Schatten-von Neumann Classes and Trace Class
  • Pointwise Estimates for Integral Kernels
  • Dirac-Type
  • Derivation of the Trace Formula - The Trace Class Result
  • Derivation of the Trace Formula - Diagonal Estimates
  • The Case n = 3
  • The Index Theorem and Some Consequences
  • Perturbation Theory for the Helmholtz Equation
  • The Proof of Theorem 10.2: The Smooth Case
  • The Proof of Theorem 10.2: The General Case
  • A Particular Class of Non-Fredholm Operators L and Their Generalized Witten Index
  • A: Construction of the Euclidean Dirac Algebra
  • B: A Counterexample to [22, Lemma 5]
  • References
  • Index.

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