Riya Ghosh

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20232026

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5 papers · 1 filter

math.FA2026

Gabor Frame Regions and Non-Frame Obstructions for an even Rational Window

Riya Ghosh

We study the Gabor frame properties of the rational window $g (x) = \frac{x ^{2} - 1}{( x ^{2} + 1 ) ( x ^{2} + 4 ) ( x ^{2} + 9 )},$ whose poles occur in symmetric pairs. We prove that every lattice satisfy…

math.FA2026

Sampling and Density Theorems for the Fractional Opdam-Cherednik Transform

Riya Ghosh, Anirudha Poria

In this paper, we establish sampling and density results for the fractional Opdam-Cherednik transform. Using the Sturm-Liouville structure of Jacobi functions, we construct a Riesz…

math.FA2026

Gabor Frames for a Rational Window with Symmetric Poles

Riya Ghosh

We investigate the Gabor frame problem for a rational window $g (x) = \frac{x}{( x ^{2} + 1 ) ( x ^{2} + 4 )} .$ This window falls outside the classes covered by existing frame set characterizatio…

math.FA2023

Obstructions for Gabor frames of the second order B-spline

Riya Ghosh, A. Antony Selvan

For a window $g \in L^{2} (R)$ , the subset of all lattice parameters $(a, b) \in R_{+}^{2}$ such that $\mathcal{G}(g,a,b)=\{e^{2πib m\cdot}g(\cdot-a k) : k, m\in\mathbb{Z}…

math.FA2023

On Gabor frames generated by B-splines, totally positive functions, and Hermite functions

Riya Ghosh, A. Antony Selvan

The frame set of a window $ϕ \in L^{2} (R)$ is the subset of all lattice parameters $(α, β) \in R_{+}^{2}$ such that $\mathcal{G}(ϕ,α,β)=\{e^{2πiβm\cdot}ϕ(\cdot-αk) : k, m…