Möbius covariance of iterated Dirac operators

Möbius fitting aggregation operators

Standard Mobius transform evaluation formula for the Choquet integral is associated with the min-aggregation. However, several other aggregation operators replacing min operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all...

Dirac Operators

p-Dirac Operators

We introduce non-linear Dirac operators in R associated to the p-harmonic equation and we extend to other contexts including spin manifolds and the sphere.

Higher spin Dirac operators

In Clifford analysis, one studies spin-invariant differential operators on spaces of arbitrary dimension m. At the heart of the classical theory lies the well-known Dirac operator, which finds its origin in physics [5]: the Dirac equation describes the behaviour of electrons in the 4-dimensional spacetime. Our aim is to study generalizations of this operator, the so-called higher spin Dirac ope...

Natural Equivariant Dirac Operators

We introduce a new class of natural, explicitly defined, transversally elliptic differential operators over manifolds with compact group actions. Under certain assumptions, the symbols of these operators generate all the possible values of the equivariant index. We also show that the components of the representation-valued equivariant index coincide with those of an elliptic operator constructe...