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Mansi Mishra

Publications and source records attributed to Mansi Mishra.

5 recordsLinked to original sources
arXiv2026

A generalization of a result of Minakshisundaram and Pleijel

Minakshisundaram and Pleijel gave an asymptotic formula for the sum of squares of the pointwise values of the eigenfunctions of the Laplace-Beltrami operator on a compact Riemannian manifold, with eigenvalues less than a fixed number. Zelditch later extended this result by replacing the pointwise values with the Fourier coefficients of a smooth measure supported on a compact submanifold. Zelditch's result is very general, and his proof relies on the theory of Fourier integral operators. Here we give a proof based on methods of Riemannian geometry.

math.DG↗
arXiv2025

Linear independence of quantum translates

If $A$ is in the $p$-Schatten class on $\mathbb{R}^n$, $1\leq p \leq \frac{4n}{2n-1}$, then the quantum translates of $A$ are linearly independent. Moreover, there exists a non-zero operator in the $p$-Schatten class on $\mathbb{R}^n$, $p>\frac{4n}{2n-1}$ whose quantum translates are linearly dependent.

math.CA↗
arXiv2025

The Weyl transform of a compactly supported distribution

If $T$ is a compactly supported distribution on $\mathbb{R}^{2n}$, then the Weyl transform of $T$ is $p$-power traceable if and only if the Fourier transform of $T$ is $p$-power integrable, and the Weyl transform of $T$ is a compact operator if and only if the Fourier transform of $T$ vanishes at infinity.

math.CA↗
arXiv2022

The Weyl Transform of a measure

(1) Suppose $μ$ is a smooth measure on a hypersurface of positive Gaussian curvature in $\R^{2n}$. If $n\ge 2$, then $W(μ)$, the Weyl transform of $μ$, is a compact operator, and if $p>n\ge 6$ then $W(μ)$ belongs to the $p$-Schatten class. (2) There exist Schatten class operators with linearly dependent quantum translates.

math.CA↗