arXiv subjects

Durgesh Pasawan

Publications and source records attributed to Durgesh Pasawan.

3 recordsLinked to original sources

arXiv2026

Pseudo-differential operators associated with the fractional Hankel-Bessel transform

We introduce and study a new class of pseudo-differential operators associated with a fractional Hankel--Bessel transform. Motivated by the classical Hankel transform and the pseudo-differential operators associated with Bessel operators studied by Pathak and Pandey \cite{PathakPandey1995}, we define a fractional variant by inserting a fractional Fourier-type phase into the Hankel kernel. We then introduce global Shubin-type symbol classes adapted to this transform, derive kernel estimates and integral representations, and establish boundedness results on weighted L^{p}-spaces and on fractional Hankel--Sobolev spaces. This provides a new framework parallel to the classical Hankel pseudo-differential calculus, but in a fractional and global setting.

math.FA↗

arXiv2025

Pseudo-differential operators associated with the gyrator transform on modulation spaces with Shubin-type symbols

We develop a theory of pseudo-differential operators associated with the gyrator transform on modulation spaces. The gyrator transform is a two-dimensional linear canonical transform which can be viewed as a rotation in the time-frequency plane and is closely related to the fractional Fourier transform. Motivated by the global structure of the gyrator kernel, we work with Shubin global symbol classes on $\mathbb{R}^4$. We first recall basic properties of modulation spaces and establish continuity and invertibility of the gyrator transform on these spaces, using its representation as a metaplectic operator. Then we introduce pseudo-differential operators defined via the gyrator transform and a Shubin symbol, and we prove boundedness results on modulation spaces and on gyrator-based modulation-Sobolev spaces. Our work extends and generalises earlier results of Mahato, Arya and Prasad on Schwartz and Sobolev spaces \cite{MahatoGyrator} to the more flexible framework of modulation spaces.

math.FA↗

arXiv2025

SG-Hankel Pseudo-Differential Operators on Weighted Gelfand-Shilov Type Spaces and a Numerical Example

We introduce a new class of SG pseudo-differential operators associated with the Hankel transform on a family of weighted Gelfand--Shilov type spaces of radial functions. First, we recall basic properties of the Hankel transform of order $\nu>-1/2$ and define a convenient Gelfand--Shilov type space $W_{\alpha,\beta}$ which is invariant under the Hankel transform and stable under differentiation and multiplication by powers of the radial variable. Then we define the SG--Hankel symbol class $S^{m_1,m_2}_H$ and the corresponding pseudo-differential operator \[ (T_\sigma f)(x)=\int_0^\infty \sigma(x,\lambda)J_\nu(x\lambda)\widehat f_H(\lambda)\,\lambda\,d\lambda. \] We prove that $T_\sigma$ is continuous on $W_{\alpha,\beta}$, and under additional decay assumptions on the symbol, we obtain compactness results between different weighted spaces. Minimal and maximal realisations of $T_\sigma$ in $L^2((0,\infty),x\, dx)$ are studied in detail, and a weak solvability result for the SG--Hankel pseudo-differential equation $T_\sigma f=g$ is derived. Finally, we present a numerical example for a simple SG symbol and a Gaussian input, illustrating the spatial decay predicted by the theory.

math.FA↗