Dirac operators and spectral triples for some fractal sets built on curves

TY - JOUR

T1 - Dirac operators and spectral triples for some fractal sets built on curves

AU - Christensen, Erik

AU - Ivan, Cristina

AU - Lapidus, Michel L.

PY - 2008

Y1 - 2008

N2 - A spectral triple is an object which is described using an algebra of operators on a Hilbert space and an unbounded self-adjoint operator, called a Dirac operator. This model may be applied to the study of classical geometrical objects .The article contains a construction of a spectral triple associated to some classical fractal subsets of the plane, and it is demonstrated that you can read of many classical geometrical structures, such as distance, measure and Hausdorff dimension from the spectral triple.

AB - A spectral triple is an object which is described using an algebra of operators on a Hilbert space and an unbounded self-adjoint operator, called a Dirac operator. This model may be applied to the study of classical geometrical objects .The article contains a construction of a spectral triple associated to some classical fractal subsets of the plane, and it is demonstrated that you can read of many classical geometrical structures, such as distance, measure and Hausdorff dimension from the spectral triple.

KW - Faculty of Science

KW - matematik

KW - ikke kommutativ geometri

KW - mathematics

KW - non commutativ geometry

U2 - 10.1016/j.aim.2007.06.009

DO - 10.1016/j.aim.2007.06.009

M3 - Journal article

SN - 0001-8708

VL - 217

SP - 42

EP - 78

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -