arXiv subjects

Subhadip Pal

Publications and source records attributed to Subhadip Pal.

18 recordsLinked to original sources

arXiv2026

A characterization of Banach spaces with numerical index one

We investigate the extremal properties of the unit ball of $L(X)_w^*$, the dual space of bounded linear operators defined on a Banach space $X$ equipped with the numerical radius norm. As an application of the present study, we obtain a geometric characterization of Banach spaces with numerical index one, which extends the well-known McGregor's characterization of finite-dimensional Banach spaces with numerical index one. We also present refinements of several earlier results in this direction, including an explicit description of the extreme points of $B_{L(X)_w^*}$, the unit ball of $L(X)_w^*$, for any finite-dimensional Banach space $X$. This allows us to obtain an independent and elementary proof of McGregor's characterization of finite-dimensional Banach spaces with numerical index one.

math.FA↗

arXiv2026

On the geometry of $G$-norm

Let $X$ and $Y$ be Banach spaces and let $G \in L(X,Y)$ with $\|G\|=1$. We study the geometry of $G$-(semi-)norm on $L(X,Y)$, defined by \[ \|T\|_G := \inf_{\delta>0}\sup\{\|Tx\|: \|x\|=1, \|Gx\|>1-\delta\}, \] considering it as a norm ($G$-norm), and further explore the associated numerical indices. In particular, we characterize relative spear operators, that is, operators for which the numerical radius with respect to $G$ coincides with the $G$-norm. Relations among the numerical indices and their invariance under isometric isomorphisms are established. We further obtain a description of the dual unit ball of $(L(X,Y),\|\cdot\|_G)$ and characterize smooth points of its unit ball. In finite-dimensional Hilbert spaces, we prove that relative spear operators are partial isometries. Finally, we establish some equivalent criteria for which the $G$-norm is achieved by the norm attainment set of a norm-attaining operator $G$.

math.FA↗

arXiv2025

Improved reconstruction of the century-long solar magnetic field by incorporating morphological asymmetry in sunspots

Accurately modeling the solar magnetic field is important for understanding long-term solar activity and space weather, but it is challenging due to limited observations, especially near the poles. The Surface Flux Transport (SFT) model simulates how magnetic flux moves across the solar surface and contributes to the polar field, but it parametrizes emerged sunspots as simple symmetric bipolar regions and needs improvement by including more realistic sunspot features. In this study, we reconstruct the century-long evolution of the solar magnetic field, including the polar regions, using an improved SFT model. We incorporate cycle-dependent morphological asymmetry between leading and following sunspots, along with observationally derived tilt angles and sunspot area data for a century (1913-2016), to better represent magnetic flux transport and investigate the impact of asymmetry on polar field development. To study morphological asymmetry, we consider two cases: first, a long-term asymmetry factor calculated from the ratio of leading and following sunspot areas spanning over a century; second, the temporal asymmetry factor observed during solar cycle 23 applied to every solar cycle. Our simulated magnetic flux transport with inclusion of morphological asymmetry for both cases gets improved compared to the no asymmetry case in terms of enhanced low and mid-latitude magnetic flux and matches closely with observations. The simulated polar fields with asymmetry also show a better agreement with polar field observations for most cycles, particularly in capturing the timing of the polar field reversals and the peak amplitude during solar minima, which has severe consequences in solar cycle prediction

astro-ph.SR↗

arXiv2025

Measurements of $D^{0}$ and $D^{*}$ production in p+p collisions at $\sqrt{s}$ = 510 GeV in STAR experiment

These proceedings present an investigation into the production of $D^{0}$ and $D^{*}$ mesons as a function of transverse momentum in proton-proton (p+p) collisions at a center-of-mass energy of $\sqrt{s}$ = 510 GeV, in the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). Objective of this analysis is to test the perturbative QCD calculations with the charm-anticharm production cross-sections obtained through $D^{0}$ and $D^{*}$ measurements. This report includes ongoing signal extractions of the $D^{0}$ and $D^{*}$ mesons from minimum bias events recorded during the p+p collisions at $\sqrt{s}$ = 510 GeV at STAR in 2017. Signals were reconstructed through the hadronic decay channels of these mesons. Like-sign combination and track rotation methods have been used to estimate the combinatorial background for $D^{0}$ measurement from $p_{T}$ = 0.0 to 2.1 GeV/$c$. For $D^{*}$, wrong-sign and side band combination of the decay daughters were utilized to reconstruct the combinatorial background from $p_{T}$ = 2.0 to 6.0 GeV/$c$.

nucl-ex↗

arXiv2025

On multidimensional Bohr radius of finite dimensional Banach spaces

In this paper, we improve the lower estimate of multidimensional Bohr radius for unit ball of $\ell^n_q$-spaces ($1\leq q\leq \infty$) for bounded holomorphic functions with values in finite dimensional complex Banach spaces. The new estimate provides the improved lower bound for the Bohr radius which was previously given by Defant, Maestre, and Schwarting [Adv. Math. 231 (2012), 2837--2857].

math.CV↗

arXiv2024

Arithmetic Bohr radius of bounded linear operators

In this paper, we investigate the arithmetic Bohr radius of bounded linear operators between arbitrary complex Banach spaces. We establish the close connection between the classical Bohr radius and the arithmetic Bohr radius of bounded linear operators. Further, we study the asymptotic estimates of arithmetic Bohr radius for identity operator on infinite dimensional complex Banach spaces. Finally, we obtain the correct asymptotic behavior of Bohr radii of operators between sequence spaces.

math.FA↗

arXiv2024

On multidimensional Bohr radii for Banach spaces

In this paper, we study a more general version of multidimensional Bohr radii for the holomorphic functions defined on unit ball of $\ell^n_q\,\,(1\leq q\leq \infty)$ spaces with values in arbitrary complex Banach spaces. More precisely, we study the multidimensional Bohr radii for bounded linear operators between complex Banach spaces, primarily motivated by the work of A. Defant, M. Maestre, and U. Schwarting [Adv. Math. 231 (2012), pp. 2837--2857]. We obtain the exact asymptotic estimates of multidimensional Bohr radius for both finite and infinite dimensional Banach spaces. As an application, we find the lower bound of arithmetic Bohr radius.

math.FA↗

arXiv2023

A Bayesian Methodology for Estimation for Sparse Canonical Correlation

It can be challenging to perform an integrative statistical analysis of multi-view high-dimensional data acquired from different experiments on each subject who participated in a joint study. Canonical Correlation Analysis (CCA) is a statistical procedure for identifying relationships between such data sets. In that context, Structured Sparse CCA (ScSCCA) is a rapidly emerging methodological area that aims for robust modeling of the interrelations between the different data modalities by assuming the corresponding CCA directional vectors to be sparse. Although it is a rapidly growing area of statistical methodology development, there is a need for developing related methodologies in the Bayesian paradigm. In this manuscript, we propose a novel ScSCCA approach where we employ a Bayesian infinite factor model and aim to achieve robust estimation by encouraging sparsity in two different levels of the modeling framework. Firstly, we utilize a multiplicative Half-Cauchy process prior to encourage sparsity at the level of the latent variable loading matrices. Additionally, we promote further sparsity in the covariance matrix by using graphical horseshoe prior or diagonal structure. We conduct multiple simulations to compare the performance of the proposed method with that of other frequently used CCA procedures, and we apply the developed procedures to analyze multi-omics data arising from a breast cancer study.

stat.ME↗

arXiv2023

Arithmetic Bohr radius for the Minkowski space

The main aim of this paper is to study the arithmetic Bohr radius for holomophic functions defined on a Reinhardt domain in $\mathbb{C}^n$ with positive real part. The present investigation is motivated by the work of Lev Aizenberg [Proc. Amer. Math. Soc. 128 (2000), 2611--2619]. A part of our study in the present paper includes a connection between the classical Bohr radius and the arithmetic Bohr radius of unit ball in the Minkowski space $\ell^n_{q}\, , 1\leq q\leq \infty$. Further, we determine the exact value of a Bohr radius in terms of arithmetric Bohr radius.

math.CV↗

arXiv2023

Multidimensional Bohr radii for holomorphic functions with values in complex Banach spaces

The main aim of this paper is to study multidimensional Bohr radii for holomorphic functions defined in complete Reinhardt domains in $\mathbb{C}^n$ with values in complex Banach spaces. More specifically, for holomorphic functions with values in arbitrary complex Banach spaces, we explore the asymptotic estimates of the classical Bohr radius and arithmetic Bohr radius in the unit ball of $\ell^n_q$ $(1\leq q\leq \infty)$ spaces. Further, we study a mixed version of Bohr radii for vector-valued holomorphic functions and as a consequence we obtain the exact value of mixed arithmetic Bohr radius.

math.CV↗

arXiv2023

Composition-Differentiation Operator on Weighted Bergman Spaces

In this paper, we study the complex symmetry of weighted composition-differentiation operator $D_{n, \psi, \phi}$ on weighted Bergman spaces $\mathcal{A}^2_{\alpha}$ with respect to the conjugation $C_{\mu, \eta}$ for $\mu, \eta \in \{z\in \mathbb{C}:|z|=1\}$. We obtain explicit conditions for which the operator $D_{n, \psi, \phi}$ is Hermitian and normal. We also characterize the complex symmetric weighted composition-differentiation operator for derivative Hardy spaces.

math.CV↗

arXiv2022

Bohr and Rogosinski inequalities for operator valued holomorphic functions

For any complex Banach space $X$ and each $p \in [1,\infty)$, we introduce the $p$-Bohr radius of order $N(\in \mathbb{N})$ is $\widetilde{R}_{p,N}(X)$ defined by $$ \widetilde{R}_{p,N}(X)=\sup \left\{r\geq 0: \sum_{k=0}^{N}\norm{x_k}^p r^{pk} \leq \norm{f}^p_{H^{\infty}(\mathbb{D}, X)}\right\}, $$ where $f(z)=\sum_{k=0}^{\infty} x_{k}z^k \in H^{\infty}(\mathbb{D}, X)$. Here $\mathbb{D}= \{z\in \mathbb{C}: |z| <1\}$ denotes the unit disk. We also introduce the following geometric notion of $p$-uniformly $\mathbb{C}$-convexity of order $N$ for a complex Banach space $X$ for some $N \in \mathbb{N}$. In this paper, for $p\in [2,\infty)$ and each $N \in \mathbb{N}$, we prove that a complex Banach space $X$ is $p$-uniformly $\mathbb{C}$-convex of order $N$ if, and only if, the $p$-Bohr radius of order $N$ $\widetilde{R}_{p,N}(X)>0$. We also study the $p$-Bohr radius of order $N$ for the Lebesgue spaces $L^q (\mu)$ for $1\leq p<q<\infty$ or $1\leq q \leq p <2$. Finally, we prove an operator valued analogue of a refined version of Bohr and Rogosinski inequality for bounded holomorphic functions from the unit disk $\mathbb{D}$ into $\mathcal{B(\mathcal{H})}$, where $\mathcal{B(\mathcal{H})}$ denotes the space of all bounded linear operator on a complex Hilbert space $\mathcal{H}$.

math.FA↗

arXiv2021

On the extended version of Krasnosel'skii's fixed point theorem for Kannan type equicontraction mappings

A sufficient condition is established for the existence of a solution to the equation $\mathcal{T}(u,\mathcal{C}(u))=u$, by considering a class of Kannan type equicontraction mappings $\mathcal{T}:\mathcal{A}\times \overline{\mathcal{C}(\mathcal{A})}\to \Xi$, where $\mathcal{A}$ is a convex, closed and bounded subset of a Banach space $\Xi$ and $\mathcal{C}$ is a compact mapping. To fulfil the desired purpose, we engage the Sadovskii's theorem, involving the measure of noncompactness. The relevance of the acquired results has been illustrated by considering a certain class of initial value problems.

math.FA↗

arXiv2021

Geometric ergodicity of Gibbs samplers for the Horseshoe and its regularized variants

The Horseshoe is a widely used and popular continuous shrinkage prior for high-dimensional Bayesian linear regression. Recently, regularized versions of the Horseshoe prior have also been introduced in the literature. Various Gibbs sampling Markov chains have been developed in the literature to generate approximate samples from the corresponding intractable posterior densities. Establishing geometric ergodicity of these Markov chains provides crucial technical justification for the accuracy of asymptotic standard errors for Markov chain based estimates of posterior quantities. In this paper, we establish geometric ergodicity for various Gibbs samplers corresponding to the Horseshoe prior and its regularized variants in the context of linear regression. First, we establish geometric ergodicity of a Gibbs sampler for the original Horseshoe posterior under strictly weaker conditions than existing analyses in the literature. Second, we consider the regularized Horseshoe prior introduced in Piironen and Vehtari (2017), and prove geometric ergodicity for a Gibbs sampling Markov chain to sample from the corresponding posterior without any truncation constraint on the global and local shrinkage parameters. Finally, we consider a variant of this regularized Horseshoe prior introduced in Nishimura and Suchard (2020), and again establish geometric ergodicity for a Gibbs sampling Markov chain to sample from the corresponding posterior.

math.ST↗

arXiv2019

A Bayesian Approach for Analyzing Data on the Stiefel Manifold

Directional data emerges in a wide array of applications, ranging from atmospheric sciences to medical imaging. Modeling such data, however, poses unique challenges by virtue of their being constrained to non-Euclidean spaces like manifolds. Here, we present a unified Bayesian framework for inference on the Stiefel manifold using the Matrix Langevin distribution. Specifically, we propose a novel family of conjugate priors and establish a number of theoretical properties relevant to statistical inference. %Importantly, these include the propriety of these priors and concentration characterization. Conjugacy enables the translation of these properties to their corresponding posteriors, which we exploit to develop the posterior inference scheme. For the implementation of the posterior computation, including the posterior sampling, we adopt a novel computational procedure for evaluating the hypergeometric function of matrix arguments that appears as normalization constants in the relevant densities.

math.ST↗

arXiv2019

Multiplicity dependence of strange and multi-strange hadrons in p$-$p, p$-$Pb and Pb$-$Pb collisions at LHC energies using Tsallis-Weibull Formalism

The transverse momentum ($p_{T}$) distribution of strange hadrons ($K_{S}^{0}$ and $\Lambda$) and multi-strange hadrons( $\Xi$ and $\Omega$) measured in p$-$p, p$-$Pb, and Pb$-$Pb collisions at LHC energies have been studied for different multiplicity classes using Tsallis-Weibull (or q$-$Weibull)formalism. The distribution describes the measured $p_{T}$ spectra for all multiplicity (or centrality)classes. The multiplicity dependence of the extracted parameters are studied for the mentioned collisions systems. The $\lambda$ parameter was observed to increase systematically with the collision multiplicity and follows a mass hierarchy for all collision system. This characteristic feature indicates that $\lambda$ can be associated to the strength of collectivity for heavy ion collisions. It can also be related to strength of dynamic effects such as multi-partonic interactions and color reconnections which mimic collectivity in smaller systems. The non-extensive $q$ parameter is found to be greater than one for all the particles suggesting that the strange particles are emitted from a source which is not fully equilibrated.

hep-ph↗

arXiv2018

Effect of Rope Hadronisation on Strangeness Enhancement in p$-$p collisions at LHC energies

The p$-$p collisions at high multiplicity at LHC show small scale collective effects similar to that observed in heavy ion collisions such as enhanced production of strange and multi-strange hadrons, long range azimuthal correlations, etc. The observation of strangeness enhancement in p$-$p collisions at at $\sqrt{s}$ = 7 TeV and 13 TeV as measured by ALICE experiment is explored using Pythia8 event generator within the framework of microscopic rope hadronization model which assumes the formation of ropes due to overlapping of strings in high multiplicity environment. The transverse momentum ($p_{T}$) spectra shape and its hardening with multiplicity is well described by the model. The mechanism of formation of ropes also described the observed experimental strangeness enhancement for higher multiplicity classes in p$-$p collisions at 7 TeV and 13 TeV. The enhancement with multiplicity is further investigated by studying the mean $p_{T}$ ($ $) and the integrated yields ($ $ ) of strange and multi-strange hadrons and comparing the predictions to the measured data at LHC for 7 TeV and 13 TeV.

hep-ph↗

arXiv2017

A Bayesian Mixture Model for Clustering on the Stiefel Manifold

Analysis of a Bayesian mixture model for the Matrix Langevin distribution on the Stiefel manifold is presented. The model exploits a particular parametrization of the Matrix Langevin distribution, various aspects of which are elaborated on. A general, and novel, family of conjugate priors, and an efficient Markov chain Monte Carlo (MCMC) sampling scheme for the corresponding posteriors is then developed for the mixture model. Theoretical properties of the prior and posterior distributions, including posterior consistency, are explored in detail. Extensive simulation experiments are presented to validate the efficacy of the framework. Real-world examples, including a large scale neuroimaging dataset, are analyzed to demonstrate the computational tractability of the approach.

stat.ME↗