D. Patel

activity

20192025

most citedRandom Sampling in reproducing kernel subspaces of

L^{p} (R^{n})

23 citations · 36 across the 7 of their papers we have counts for

collaborators

9 papers

math.FA2025

Constructive Approximation in Mixed norm Spaces

Priyanka Majethiya, Shivam Bajpeyi, Dhiraj Patel

The concept of mixed norm spaces has emerged as a significant interest in fields such as harmonic analysis. In addition, the problem of function approximation through sampling seri…

cs.LG2025

Convergence of gradient based training for linear Graph Neural Networks

Dhiraj Patel, Anton Savostianov, Michael T. Schaub

Graph Neural Networks (GNNs) are powerful tools for addressing learning problems on graph structures, with a wide range of applications in molecular biology and social networks. Ho…

math.FA2023

Random Sampling of Mellin Band-limited Signals

Shivam Bajpeyi, Dhiraj Patel, S. Sivananthan

In this paper, we address the random sampling problem for the class of Mellin band-limited functions BT which is concentrated on a bounded cube. It is established that any function…

math.NT2023

An explicit sub-Weyl bound for $ζ (1/2 + i t)$

Dhir Patel, Andrew Yang

In this article we prove an explicit sub-Weyl bound for the Riemann zeta function $ζ (s)$ on the critical line $s = 1/2 + i t$ . In particular, we show that $|ζ(1/2 + it)| \le 66.7\,…

math.NT2022

An improved explicit estimate for $ζ (1/2 + i t)$

Ghaith A. Hiary, Dhir Patel, Andrew Yang

An explicit subconvex bound for the Riemann zeta function $ζ (s)$ on the critical line $s = 1/2 + i t$ is proved. Previous subconvex bounds relied on an incorrect version of the Kusmin-L…

math.FA2021★ 3 cited

Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of $L^{p} (R^{n})$

Dhiraj Patel, S. Sivananthan

The paper is devoted to studying the stability of random sampling in a localized reproducing kernel space. We show that if the sampling set on $Ω$ (compact) discretizes the integra…

math.FA2021★ 8 cited

Random Sampling in Reproducing Kernel Subspace of Mixed Lebesgue Spaces

Prashant Goyal, Dhiraj Patel, Sivananthan Sampath

In this article, we consider the random sampling in the image space $V$ of mixed Lebesgue space $L^{p, q} (R^{n + 1})$ under an idempotent integral operator. We assume some de…

math.NT2020★ 2 cited

An Explicit Upper Bound for $∣ ζ (1 + i t) ∣$

Dhir Patel

In this paper we provide an explicit bound for $∣ ζ (1 + i t) ∣$ in the form of $∣ ζ (1 + i t) ∣ \leq min (lo g t, \frac{1}{2} lo g t + 1.93, \frac{1}{5} lo g t + 44.02)$ . This improves o…

math.FA2019★ 23 cited

Random Sampling in reproducing kernel subspaces of $L^{p} (R^{n})$

Dhiraj Patel, Sivananthan Sampath

In this paper, we study random sampling on reproducing kernel space $V$ , which is a range of an idempotent integral operator. Under certain decay condition on the integral kernel,…

Constructive Approximation in Mixed norm Spaces

Convergence of gradient based training for linear Graph Neural Networks

Random Sampling of Mellin Band-limited Signals

An explicit sub-Weyl bound for ζ(1/2+it)

An improved explicit estimate for ζ(1/2+it)

Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of Lp(Rn)