arXiv subjects
Publications and source records attributed to Yash Rastogi.
We prove a Weyl-type theorem for the Kohn Laplacian on sphere quotients as CR manifolds. We show that we can determine the fundamental group from the spectrum of the Kohn Laplacian in dimension three. Furthermore, we prove Sobolev estimates for the complex Green's operator on these quotient manifolds.
In this paper, we present a multidimensional, highly effective method for aggregating data for wireless sensor networks while maintaining privacy. The suggested system is resistant to data loss and secure against both active and passive privacy compromising attacks, such as the coalition attack from a rogue base station and kidnapped sensor nodes. With regard to cluster size, it achieves consistent communication overhead, which is helpful in large-scale WSNs. Due to its constant size communication overhead, the suggested strategy outperforms the previous privacy-preserving data aggregation scheme not only in terms of privacy preservation but also in terms of communication complexity and energy costs.
The conversion of resolvent conditions into semigroup estimates is crucial in the stability analysis of hyperbolic partial differential equations. For two families of multiple Toeplitz operators, we relate the power bound with a resolvent condition of Kreiss-Ritt type. Furthermore, we show that the power bound is bounded above by a polynomial of the resolvent condition. The operators under investigation do not fall into a well-understood class, so our analysis utilizes explicit reproducing kernel techniques. Our methods apply \textit{mutatis mutandis} to composites of Toeplitz operators with polynomial symbol, which arise frequently in the numerical solution of initial value problems encountered in science and engineering.