17 citations · 77 across the 17 of their papers we have counts for
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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…
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…
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…
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…
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…