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D-bar and Dirac Type Operators on Classical and Quantum Domains
Dirac Operators Noncommutative Geometry
2015/1/19
I study d-bar and Dirac operators on classical and quantum domains subject to the APS boundary conditions, APS like boundary conditions, and other types of global boundary conditions. Moreover, the in...
A Note on Gluing Dirac Type Operators on a Mirror Quantum Two-Sphere
Gluing Dirac Type Operators Mirror Quantum Two-Sphere
2014/12/12
The goal of this paper is to introduce a class of operators, which we call quantum Dirac type operators on a noncommutative sphere, by a gluing construction from copies of noncommutative disks, subjec...
Quadratic estimates for perturbed Dirac type operators on doubling measure metric spaces
Quadratic estimates holomorphic functional calculi doubling measure measure metric space Dirac type operators
2011/9/15
Abstract: We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for...
Abstract Wave Equations and Associated Dirac-Type Operators
Dirac operators supersymmetry wave equations semigroups
2011/2/25
We discuss the unitary equivalence of generators GA,R associated with abstract damped wave equations of the type u¨+Ru˙ +AAu = 0 in some Hilbert space H1 and certain non-self-adjoint Dirac-type opera...