# Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves

@article{Landry2021MetricAO, title={Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves}, author={Therese-Marie Landry and Michel L. Lapidus and Fr{\'e}d{\'e}ric Latr{\'e}moli{\`e}re}, journal={Advances in Mathematics}, year={2021} }

## 3 Citations

Classical Multidimensional Scaling on Metric Measure Spaces

- Mathematics, Computer Science
- 2022

We study a generalization of the classical Multidimensional Scaling procedure (cMDS) which is applicable in the setting of general metric measure spaces which can be seen as natural “continuous…

Classical MDS on Metric Measure Spaces

- Mathematics
- 2022

. We study a generalization of the classical Multidimensional Scaling procedure (cMDS) to the setting of general metric measure spaces. We identify certain crucial spectral properties of the…

Convergence of Spectral Triples on Fuzzy Tori to Spectral Triples on Quantum Tori

- MathematicsCommunications in Mathematical Physics
- 2021

Fuzzy tori are finite dimensional C*-algebras endowed with an appropriate notion of noncommutative geometry inherited from an ergodic action of a finite closed subgroup of the torus, which are meant…

## References

SHOWING 1-10 OF 88 REFERENCES

On one effective method of solving certain classes of extremal problems

- Dokl. Akad. Nauk USSR
- 1940

Rubinstein

- On the space of completely additive functions, Vestnik Leningrad Univ., Ser. Mat. Mekh. i Astron. 13
- 1958

Dirichlet forms on fractals and products of random matrices

- Mathematics
- 1989

The author studies Dirichlet forms on fractals. He constructs some local Dirichlet forms on abstract fractal sets by using products of random matrices. Also, he studies the martingale dimension of…

Dirac operators and geodesic metric on the harmonic Sierpinski gasket and other fractal sets

- Mathematics
- 2014

We construct Dirac operators and spectral triples for certain, not necessarily self-similar, fractal sets built on curves. Connes' distance formula of noncommutative geometry provides a natural…

Analysis and geometry of the measurable Riemannian structure on the Sierpi nski gasket

- Mathematics
- 2013

This expository article is devoted to a survey of existent results concerning the measurable Riemannian structure on the Sierpi� nski gasket and to a brief account of the author's recent result on…

Vibrations of fractal drums.

- PhysicsPhysical review letters
- 1991

The low-frequency vibrations of a membrane bounded by a rigid fractal contour are observed and localized modes are found and first lower eigen modes are computed using an analogy between the wave and the diffusion equations.