# Spectral asymptotics of Kreĭn–Feller operators for weak Gibbs measures on self-conformal fractals with overlaps

@article{Kessebohmer2021SpectralAO, title={Spectral asymptotics of Kreĭn–Feller operators for weak Gibbs measures on self-conformal fractals with overlaps}, author={Marc Kessebohmer and Aljoscha Niemann}, journal={Advances in Mathematics}, year={2021} }

## 4 Citations

### Spectral dimensions of Krein-Feller operators in higher dimensions

- Mathematics
- 2022

A bstract . We study the spectral dimensions of Kre˘ın–Feller operators for ﬁnite Borel measures ν on the d -dimensional unit cube via a form approach. We introduce the notion of the spectral…

### Quantization dimensions of compactly supported probability measures via R\'enyi dimensions

- Mathematics, Computer Science
- 2022

It is proved that the upper quantization dimension D r ( ν ) of order r > 0 for an arbitrary compactly supported Borel probability measure ν is given by its R´enyi dimension at the point q r where the L q -spectrum of ν and the line through the origin with slope r intersect.

### Approximation order of Kolmogorov diameters via L-spectra and applications to polyharmonic operators

- MathematicsJournal of Functional Analysis
- 2022

### Spectral dimensions of Kreĭn–Feller operators and L-spectra

- MathematicsAdvances in Mathematics
- 2022

## References

SHOWING 1-10 OF 58 REFERENCES

### On multifractal formalism for self-similar measures with overlaps

- MathematicsMathematische Zeitschrift
- 2020

Let μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

### Spectral dimensions of Kreı̆n–Feller operators and Lq-spectra

- Adv. Math. 399, Paper No. 108253
- 2022

### Some consideration of asymptotic distribution of eigenvalues for the equation d2u/dx2+λρ(x)u=0

- Mathematics
- 1959

### An Improved Multifractal Formalism and Self Affine Measures

- Mathematics
- 1993

To characterize the geometry of a probability measure fi with bounded support, its so-called spectrum / has been introduced recently. A mathematically precise definition has been given in [Falc4]:…

### An Improved Multifractal Formalism and Self Similar Measures

- Mathematics
- 1995

Abstract To characterize the geometry of a measure, its generalized dimensions dq have been introduced recently. The mathematically precise definition given by Falconer ["Fractal Geometry," 1990]…

### A fractional dimension, self-similarity and a generalized diffusion operator, in: Probabilistic methods in mathematical physics (Katata/Kyoto

- 1987

### Spectral dimensions of Krein-Feller operators in higher dimensions

- Mathematics
- 2022

A bstract . We study the spectral dimensions of Kre˘ın–Feller operators for ﬁnite Borel measures ν on the d -dimensional unit cube via a form approach. We introduce the notion of the spectral…

### Approximation order of Kolmogorov diameters via L-spectra and applications to polyharmonic operators

- MathematicsJournal of Functional Analysis
- 2022