Dirac operators and spectral triples for some fractal sets built on curves
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Dirac operators and spectral triples for some fractal sets built on curves. / Christensen, Erik; Ivan, Cristina; Lapidus, Michel L.
In: Advances in Mathematics, Vol. 217, No. 1, 2008, p. 42 - 78.Research output: Contribution to journal › Journal article › Research › peer-review
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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
VL - 217
SP - 42
EP - 78
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
IS - 1
ER -
ID: 1631998