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

@article{Kessebhmer2021ApproximationOO, title={Approximation order of Kolmogorov diameters via L-spectra and applications to polyharmonic operators}, author={Marc Kesseb{\"o}hmer and Aljoscha Niemann}, journal={Journal of Functional Analysis}, year={2021} }

## 4 Citations

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

- MathematicsAdvances in Mathematics
- 2022

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

- MathematicsAdvances in Mathematics
- 2022

### 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.

## References

SHOWING 1-10 OF 44 REFERENCES

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

- MathematicsAdvances in Mathematics
- 2022

### Eigenvalue estimates for a class of operators related to self-similar measures

- Mathematics
- 1994

We obtain the sharp order of growth of the eigenvalue distribution function for the operator in the Sobolev space H^{X), generated by the quadratic form f^ H^, where X C R^ is a domain and p, is a…

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

- MathematicsAdvances in Mathematics
- 2022

### Spectral Asymptotics of Laplacians Associated with One-dimensional Iterated Function Systems with Overlaps

- MathematicsCanadian Journal of Mathematics
- 2011

Abstract We set up a framework for computing the spectral dimension of a class of one-dimensional self-similar measures that are defined by iterated function systems with overlaps and satisfy a…

### $L^{q}$ -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…

### Fractal drum, inverse spectral problems for elliptic operators and a partial resolution of the Weyl-Berry conjecture

- Mathematics
- 1991

Let Í2 be a bounded open set of E" (n > 1) with "fractal" boundary T . We extend Hermann Weyl's classical theorem by establishing a precise remainder estimate for the asymptotics of the eigenvalues…

### 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…

### 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…

### On Furstenberg's intersection conjecture, self-similar measures, and the Lq norms of convolutions

- MathematicsAnnals of Mathematics
- 2019

We study a class of measures on the real line with a kind of self-similar structure, which we call dynamically driven self-similar measures, and contain proper self-similar measures such as Bernoulli…