scholarly journals Theorem of Completeness for a Dirac-Type Operator with Generalized λ-Depending Boundary Conditions

2009 ◽  
Vol 64 (3) ◽  
pp. 357-379 ◽  
Author(s):  
Seppo Hassi ◽  
Leonid Oridoroga
Keyword(s):  
Boundary Conditions ◽  
Type Operator ◽  
Dirac Type ◽  
Dirac Type Operator

A Dirac Type Operator on the Non-Commutative Disk

2010 ◽  
Vol 93 (2) ◽  
pp. 107-125 ◽  
Author(s):  
Alan L. Carey ◽  
Sławomir Klimek ◽  
Krzysztof P. Wojciechowski
Keyword(s):  
Type Operator ◽  
Dirac Type ◽  
Dirac Type Operator

scholarly journals Index Theory and Non-Commutative Geometry II. Dirac Operators and Index Bundles

2007 ◽  
Vol 1 (2) ◽  
pp. 305-356 ◽  
Author(s):  
Moulay-Tahar Benameur ◽  
James L. Heitsch
Keyword(s):  
Chern Character ◽  
Index Theory ◽  
Dirac Operators ◽  
Type Operator ◽  
Index Formula ◽  
Dirac Type ◽  
Dirac Type Operator ◽  
Index Bundle

AbstractWhen the index bundle of a longitudinal Dirac type operator is transversely smooth, we define its Chern character in Haefliger cohomology and relate it to the Chern character of the K—theory index. This result gives a concrete connection between the topology of the foliation and the longitudinal index formula. Moreover, the usual spectral assumption on the Novikov-Shubin invariants of the operator is improved.

scholarly journals Dirac-like operators on the Hilbert space of differential forms on manifolds with boundaries

2017 ◽  
Vol 14 (08) ◽  
pp. 1740004 ◽  
Author(s):  
Juan Manuel Pérez-Pardo
Keyword(s):  
Hilbert Space ◽  
Boundary Conditions ◽  
Differential Forms ◽  
Dirac Type ◽  
Dimension 2

The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analyzed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like potentials, in manifolds of dimension higher than one. Self-adjoint boundary conditions for the case of dimension 2 are obtained explicitly.

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