Amlan Banaji

activity

20242026

collaborators

12 papers

math.DS2026

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 $I^¼$ on $R^{k}$ under nonlinear smooth maps $f : R^{k} \to R$ . For…

math.DS2026

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 $I^¼$ on $R^{k}$ under sufficiently nonlinear real-analytic maps $f \colon…

math.CA2026

Attainable forms of lower spectra

Amlan Banaji, Haipeng Chen, Alex Rutar +1

Let $d \in N$ and $I ¨ : (0, 1) \to [0, d]$ . We prove there exists a set $F \subset R^{d}$ whose lower spectrum $dim^{I^} ¸_{L} F$ satisfies $(1-Î¸)\o…

math.DS2026

Self-similar and self-conformal measures with slow Fourier decay

Simon Baker, Amlan Banaji

Given any function $I ¨ : [0, \infty) \to (0, 1]$ satisfying $lim_{I^¾ \to \infty} I ¨ (I^¾) = 0$ , we prove the existence of i) self-similar measures and ii) nonlinear $C^{\infty}$ self-…

math.DS2025

Assouad spectrum of Gatzouras-Lalley carpets

Amlan Banaji, Jonathan M. Fraser, IstvÃ¡n KolossvÃ¡ry +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…

math.DS2025

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,…