Dimensions and singular traces for spectral triples, with applications to fractals
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Publication:1413977
DOI10.1016/S0022-1236(03)00230-1zbMath1031.46081arXivmath/0202108MaRDI QIDQ1413977
Publication date: 17 November 2003
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0202108
Fractals in the real linenoncommutative Hausdorff dimensionsNoncommutative Hausdorff-Besicovitch functionalSingular tracesSpectral triples
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Cites Work
- Symmetric functionals and singular traces
- Noncommutative Riemann integration and Novikov-Shubin invariants for open manifolds
- Generalized s-numbers of \(\tau\)-measurable operators
- Spectral flow and Dixmier traces
- Singular traces on semifinite von Neumann algebras
- Singular traces and compact operators
- Random Recursive Constructions: Asymptotic Geometric and Topological Properties
- Traces on Irregular Ideals
- The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums
- Generalized Minkowski content, spectrum of fractal drums, fractal strings and the Riemann zeta-function
- ON THE DOMAIN OF SINGULAR TRACES
- A remark on trace properties of K-cycles
- Lacunarity of self-similar and stochastically self-similar sets
- Interpolation zwischen den Klassen 𝔖p von Operatoren in Hilberträumen
- Self-similarity of volume measures for Laplacians on p. c. f. self-similar fractals
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