## 4 Citations

### 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.

### 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

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

- MathematicsAdvances in Mathematics
- 2022

## References

SHOWING 1-10 OF 96 REFERENCES

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

- MathematicsJournal of Functional Analysis
- 2022

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

- MathematicsAdvances in Mathematics
- 2022

### Spectral asymptotics of Laplacians related to one-dimensional graph-directed self-similar measures with overlaps

- Mathematics
- 2020

For the class of graph-directed self-similar measures on R, which could have overlaps but are essentially of finite type, we set up a framework for deriving a closed formula for the spectral…

### Estimates for sums and gaps of eigenvalues of Laplacians on measure spaces

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2021

Abstract For Laplacians defined by measures on a bounded domain in ℝn, we prove analogues of the classical eigenvalue estimates for the standard Laplacian: lower bound of sums of eigenvalues by Li…

### 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}…

### Generalised Krein-Feller operators and gap diffusions via transformations of measure spaces

- Mathematics
- 2019

A bstract . We consider the generalised Kre˘ın–Feller operator ∆ ν,µ with respect to compactly supported Borel probability measures µ and ν with the natural restrictions that µ is atomless, the supp(…

### Thesis

- Biology
- 2002

This review is the report of a single experimental protocol on the nature, structure and mechanical strength of 136 bone samples from the vertebral body of 9 subjects, which combined mechanical testing with density measurements, a study of some microarchitectural parameters and a biochemical analysis of bone collagen.

### $L^{q}$ -SPECTRUM OF SELF-SIMILAR MEASURES WITH OVERLAPS IN THE ABSENCE OF SECOND-ORDER IDENTITIES

- MathematicsJournal of the Australian Mathematical Society
- 2018

For the class of self-similar measures in $\mathbb{R}^{d}$ with overlaps that are essentially of finite type, we set up a framework for deriving a closed formula for the $L^{q}$ -spectrum of the…

### Spectral Asymptotics of One-Dimensional Fractal Laplacians in the Absence of Second-Order Identities

- Mathematics
- 2018

We observe that some self-similar measures defined by finite or infinite iterated function systems with overlaps are in certain sense essentially of finite type, which allows us to extract useful…

### Fractal Laplacians on the Unit Interval

- Physics
- 2003

Nous etudions les valeurs/fonctions propres du Laplacien sur [0, 1] definies par des mesures positives μ bornees, continues, supportees par [0, 1] et par la forme de Dirichlet classique sur [0, 1].…