17 citations · 77 across the 17 of their papers we have counts for
17 papers
Fourier transform of nonlinear images of self-similar measures: qualitative aspects
Amlan Banaji, Han Yu
The goal of this paper is to establish polynomial Fourier decay for images of self-similar measures on under sufficiently nonlinear real-analytic maps $f \colon…
Attainable forms of lower spectra
Amlan Banaji, Haipeng Chen, Alex Rutar +1
Let and . We prove there exists a set whose lower spectrum satisfies $(1-θ)\oper…
Self-similar and self-conformal measures with slow Fourier decay
Simon Baker, Amlan Banaji
Given any function satisfying , we prove the existence of i) self-similar measures and ii) nonlinear self-conf…
Distinct dimensions for attractors of bi-Lipschitz iterated function systems
Simon Baker, Amlan Banaji, De-Jun Feng +2
In this paper, we construct an iterated function system on the line consisting of two bi-Lipschitz contractions whose attractor has distinct lower, Hausdorff, lower box, upper box,…
Fourier transform of nonlinear images of self-similar measures: quantitative aspects
Amlan Banaji, Han Yu
This paper relates to the Fourier decay properties of images of self-similar measures on under nonlinear smooth maps . For…
Interpolating between Hausdorff and box dimension
Amlan Banaji
Hausdorff and box dimension are two familiar notions of fractal dimension. Box dimension can be larger than Hausdorff dimension, because in the definition of box dimension, all set…
Lower box dimension of infinitely generated self-conformal sets
Amlan Banaji, Alex Rutar
Let be the limit set of an infinite conformal iterated function system and let denote the set of fixed points of the maps. We prove that the box dimension of exists if…
Assouad spectrum of Gatzouras-Lalley carpets
Amlan Banaji, Jonathan M. Fraser, István Kolossváry +1
We study the fine local scaling properties of a class of self-affine fractal sets called Gatzouras-Lalley carpets. More precisely, we establish a formula for the Assouad spectrum o…
Polynomial Fourier decay for fractal measures and their pushforwards
Simon Baker, Amlan Banaji
We prove that the pushforwards of a very general class of fractal measures on under a large family of non-linear maps exhi…
Interpolating with generalized Assouad dimensions
Amlan Banaji, Alex Rutar, Sascha Troscheit
The -Assouad dimensions are a family of dimensions which interpolate between the upper box and Assouad dimensions. They are a generalization of the well-studied Assouad spectrum…
Dimensions of popcorn-like pyramid sets
Amlan Banaji, Haipeng Chen
This article concerns the dimension theory of the graphs of a family of functions which include the well-known 'popcorn function' and its pyramid-like higher-dimensional analogues.…
Metric Spaces where Geodesics are Never Unique
Amlan Banaji
This article concerns a class of metric spaces, which we call multigeodesic spaces, where between any two distinct points there exist multiple distinct minimising geodesics. We pro…
Assouad type dimensions of infinitely generated self-conformal sets
Amlan Banaji, Jonathan M. Fraser
We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of conformal contractions. Our focus is on the Assouad type dimen…
Attainable forms of intermediate dimensions
Amlan Banaji, Alex Rutar
The intermediate dimensions are a family of dimensions which interpolate between the Hausdorff and box dimensions of sets. We prove a necessary and sufficient condition for a given…
Intermediate dimensions of Bedford-McMullen carpets with applications to Lipschitz equivalence
Amlan Banaji, István Kolossváry
Intermediate dimensions were recently introduced to provide a spectrum of dimensions interpolating between Hausdorff and box-counting dimensions for fractals where these differ. In…
Intermediate dimensions of infinitely generated attractors
Amlan Banaji, Jonathan M. Fraser
We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of contractions. Our primary focus is on the intermediate dimensi…
Generalised intermediate dimensions
Amlan Banaji
We introduce a family of dimensions, which we call the -intermediate dimensions, that lie between the Hausdorff and box dimensions and generalise the intermediate dimensions int…