scientific article; zbMATH DE number 1072427

zbMath0889.58012MaRDI QIDQ4359323

Michel L. Lapidus

Publication date: 22 June 1998

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

self-similar setsDixmier traceHausdorff dimensionsMinkowski dimensionsoscillatory phenomenaConnes' noncommutative geometryspectral dimensionsquantized calculusanalysis and PDEs on fractalsclassical vs. quantum spacecomplex dimensions of fractalsLaplacians and volume measures on fractalsvibrations of fractal drumsvolume measures

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Noncommutative topology (46L85) Noncommutative differential geometry (46L87) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Pseudodifferential and Fourier integral operators on manifolds (58J40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Diffusion processes and stochastic analysis on manifolds (58J65) Fractals (28A80) Waves and radiation in optics and electromagnetic theory (78A40)

Related Items (15)

Eigenvalues of singular measures and Connes' noncommutative integration ⋮ Dixmier traces and non-commutative analysis ⋮ Isometries of Kellendonk–Savinien spectral triples and Connes metrics ⋮ Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis ⋮ Spectral metric spaces for Gibbs measures ⋮ Dirac operators and spectral triples for some fractal sets built on curves ⋮ Examples of infinite direct sums of spectral triples ⋮ Fractal zeta functions and complex dimensions of relative fractal drums ⋮ Spectral triples and wavelets for higher-rank graphs ⋮ A spectral triple for a solenoid based on the Sierpinski gasket ⋮ Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves ⋮ A classification of aperiodic order via spectral metrics and Jarník sets ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back ⋮ Spectral triples for the variants of the Sierpiński gasket ⋮ Gradients on fractals

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