4 papers · 2 filters
Some results on Lower Assouad and quantization dimensions
Saurabh Verma, Ekta Agrawal, Shivam Dubey
In this paper, we first show that the collection of all subsets of \( \mathbb{R} \) having lower dimension \( γ\in [0,1] \) is dense in \( Π(\mathbb{R}) \), the space of compact su…
Dimension Of Inhomogeneous Sub-Self-Similar Sets
Shivam Dubey, Saurabh Verma
In this paper, we introduce the concept of Inhomogeneous sub-self-similar (ISSS) sets, building upon the foundations laid by Falconer (Trans. Amer. Math. Soc. 347 (1995) 3121-3129)…
Quantization for a condensation system
Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma
For a given , the quantization dimension of order , if it exists, denoted by , represents the rate at which the th quantization error of order …
Quantization dimension for a generalized inhomogeneous bi-Lipschitz iterated function system
Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma
For a given , the quantization dimension of order , if it exists, denoted by , of a Borel probability measure on represents the sp…