A. G. Farashahi

activity

20122025

most citedConvolution and involution on function spaces of homogeneous spaces

15 citations · 18 across the 15 of their papers we have counts for

collaborators

16 papers

math.NA2025

Fast Convolutions on $Z^{2} \ S E (2)$ via Radial Translational Dependence and Classical FFT

Arash Ghaani Farashahi, Gregory S. Chirikjian

Let $Z^{2} \ S E (2)$ denote the right coset space of the subgroup consisting of translational isometries of the orthogonal lattice $Z^{2}$ in the non-Abelian g…

math-ph2025

Coherent manifolds

Arnold Neumaier, Phillip Josef Bachler, Arash Ghaani Farashahi

This paper defines coherent manifolds and discusses their properties and their application in quantum mechanics. Every coherent manifold with a large group of symmetries gives rise…

math.FA2024

Non-Abelian Fourier Analysis on $Γ \ S E (d)$

Arash Ghaani Farashahi, Gregory S. Chirikjian

This paper presents a systematic study for the general theory of non-Abelian Fourier series of integrable functions on the homogeneous space $Γ \ S E (d)$ , where $SE(d…

math.FA2021

Banach Convolution Modules of Group Algebras on Covariant Functions of Characters of Normal Subgroups

Arash Ghaani Farashahi

This paper investigates structure of Banach convolution modules induced by group algebras on covariant functions of characters of closed normal subgroups. Let $G$ be a locally comp…

math.FA2021

Harmonic Analysis of Covariant Functions of Characters of Normal Subgroups

Arash Ghaani Farashahi

Let $G$ be a locally compact group with the group algebra $L^{1} (G)$ and $N$ be a closed normal subgroup of $G$ . Suppose that $ξ : N \to T$ is a continuous character and $L_ξ^1(…

math.FA2019

Abstract Structure of Measure Algebras on Coset Spaces of Compact Subgroups in Locally Compact Groups

Arash Ghaani Farashahi

This paper presents a systematic operator theory approach for abstract structure of Banach measure algebras over coset spaces of compact subgroups. Let $H$ be a compact subgroup of…

math.FA2019

Discrete Spectra of Convolutions on Disks using Sturm-Liouville Theory

Arash Ghaani Farashahi, Gregory S. Chirikjian

This paper presents a systematic study for analytic aspects of discrete spectra methods for convolution of functions supported on disks, according to the Sturm-Liouville theory. We…

math.FA2018

Fourier-Zernike Series of Convolutions on Disks

Arash Ghaani Farashahi, Gregory S. Chirikjian

This paper presents a systematic study for analytic aspects of Fourier-Zernike series of convolutions of functions supported on disks. We then investigate different aspects of the…

math.FA2018

Non-Abelian Fourier Series on $Z^{2} \ S E (2)$

Arash Ghaani Farashahi, Gregory S. Chirikjian

This paper discusses computational structure of coefficients of non-Abelian Fourier series on the right coset space $Z^{2} \ S E (2)$ expressed in the trigonometric ba…

cs.CV2018

Exploiting Partial Structural Symmetry For Patient-Specific Image Augmentation in Trauma Interventions

Javad Fotouhi, Mathias Unberath, Giacomo Taylor +7

In unilateral pelvic fracture reductions, surgeons attempt to reconstruct the bone fragments such that bilateral symmetry in the bony anatomy is restored. We propose to exploit thi…

math-ph2018

Introduction to coherent quantization

Arnold Neumaier, Arash Ghaani Farashahi

This paper is one of a series of papers on coherent spaces and their applications, defined in the recent book 'Coherent Quantum Mechanics' by the first author. The paper studies co…

math.FA2012

Continuous Gabor transform for semi-direct product of locally compact groups

Arash Ghaani Farashahi

Let $H$ be a locally compact group, $K$ be an LCA group, $τ : H \to A u t (K)$ be a continuous homomorphism and $G_{τ} = H ⋉_{τ} K$ be the semi-direct product of $H$ and $K$ with respect t…

math.FA2012

A new approach to convolution and semi-direct products of groups

Arash Ghaani Farashahi, Rajabali Kamyabi-Gol

Let $H$ and $K$ be locally compact groups and $τ : H \to A u t (K)$ be a continuous homomorphism and also let $G_{τ} = H ⋉_{τ} K$ be the semi-direct product of $H$ and $K$ with respect to…

math.FA2012★ 15 cited

Convolution and involution on function spaces of homogeneous spaces

Arash Ghaani Farashahi

Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$ . It is shown that, if $μ$ is a relatively invariant measure on $G / H$ then there is a well-defined c…

math.FA2012

Continuous Gabor transform for a class of non-Abelian groups

Arash Ghaani Farashahi, Rajabali Kamyabi-Gol

In this article we define the continuous Gabor transform for second countable, non-abelian, unimodular and type I groups and also we investigate a Plancherel formula and an inversi…

math.FA2012★ 3 cited

A new approach to the Fourier analysis on semi-direct products of groups

Arash Ghaani Farashahi

Let $H$ and $K$ be locally compact groups and also $τ : H \to A u t (K)$ be a continuous homomorphism and $G_{τ} = H ⋉_{τ} K$ be the semi-direct product of $H$ and $K$ with respect to the…

Fast Convolutions on Z2\SE(2) via Radial Translational Dependence and Classical FFT

Coherent manifolds

Non-Abelian Fourier Analysis on Γ\SE(d)

Banach Convolution Modules of Group Algebras on Covariant Functions of Characters of Normal Subgroups

Harmonic Analysis of Covariant Functions of Characters of Normal Subgroups

Abstract Structure of Measure Algebras on Coset Spaces of Compact Subgroups in Locally Compact Groups

Discrete Spectra of Convolutions on Disks using Sturm-Liouville Theory

Fourier-Zernike Series of Convolutions on Disks

Non-Abelian Fourier Series on Z2\SE(2)

Exploiting Partial Structural Symmetry For Patient-Specific Image Augmentation in Trauma Interventions

Introduction to coherent quantization

Continuous Gabor transform for semi-direct product of locally compact groups

A new approach to convolution and semi-direct products of groups

Convolution and involution on function spaces of homogeneous spaces

Continuous Gabor transform for a class of non-Abelian groups

A new approach to the Fourier analysis on semi-direct products of groups

Fast Convolutions on $Z^{2} \ S E (2)$ via Radial Translational Dependence and Classical FFT

Non-Abelian Fourier Analysis on $Γ \ S E (d)$

Non-Abelian Fourier Series on $Z^{2} \ S E (2)$