15 citations · 50 across the 9 of their papers we have counts for
9 papers
Geometric mean quantization via adaptive approximation
Marc Kesseböhmer, Aljoscha Niemann
Let be a compactly supported Borel probability measure on with for some . Refine a dyadic cube exactly when its mass is at least …
Quantization dimensions of negative order
Marc Kesseböhmer, Aljoscha Niemann
We investigate the possibility of defining meaningful upper and lower quantization dimensions for a compactly supported Borel probability measure of order , including negative v…
Exact asymptotic order for generalised adaptive approximations
Marc Kesseböhmer, Aljoscha Niemann
In this note, we present an abstract approach to study asymptotic orders for adaptive approximations with respect to a monotone set function defined on dyadic cubes.…
Quantization dimensions of compactly supported probability measures via Rényi dimensions
Marc Kesseböhmer, Aljoscha Niemann, Sanguo Zhu
We provide a complete picture of the upper quantization dimension in terms of the Rényi dimension by proving that the upper quantization dimension of order f…
Spectral dimensions of Krein-Feller operators in higher dimensions
Marc Kesseböhmer, Aljoscha Niemann
We study the Dirichlet and Neumann spectral dimensions of Kreĭn-Feller operators associated with finite non-zero Borel measures supported in the open -dimensional unit cube,…
Approximation order of Kolmogorov diameters via -spectra and applications to polyharmonic operators
Marc Kesseböhmer, Aljoscha Niemann
We establish a connection between the -spectrum of a Borel measure on the -dimensional unit cube and the approximation order of Kolmogorov diameters of the unit spher…
Spectral asymptotics of Krein--Feller operators for weak Gibbs measures on self-conformal fractals with overlaps
Marc Kesseböhmer, Aljoscha Niemann
We study the spectral dimensions and spectral asymptotics of Krein--Feller operators for weak Gibbs measures on self-conformal fractals with or without overlaps. We show that, rest…
Spectral dimensions of Krein--Feller operators and -spectra
Marc Kesseböhmer, Aljoscha Niemann
We study the spectral dimensions and spectral asymptotics of Krein-Feller operators for arbitrary finite Borel measures on Connections between the spectral dime…
Generalised Krein-Feller operators and gap diffusions via transformations of measure spaces
Marc Kesseböhmer, Aljoscha Niemann, Tony Samuel +1
We consider the generalised Krein-Feller operator with respect to compactly supported Borel probability measures and with the natural restrictions that is a…