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On heat equations associated with fractional harmonic oscillators
Divyang G. Bhimani, Ramesh Manna, Fabio Nicola +2
We establish some fixed-time decay estimates in Lebesgue spaces for the fractional heat propagator , , associated with the harmonic oscillator . We…
An extension problem, trace Hardy and Hardy's inequalities for Ornstein-Uhlenbeck operator
Pritam Ganguly, Ramesh Manna, Sundaram Thangavelu
In this paper, we study an extension problem for the Ornstein-Uhlenbeck operator and we obtain various characterisations of the solution of the same. We use…
Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation
Agnid Banerjee, Ramesh Manna
In this paper, we obtain new Carleman estimates for a class of variable coefficient degenerate elliptic operators whose constant coefficient model at one point is the so called Bao…
A strong unique continuation property for the heat operator with Hardy type potential
Agnid Banerjee, Nicola Garofalo, Ramesh Manna
In this note we prove the strong unique continuation property at the origin for the solutions of the parabolic differential inequality \[ |Δu - u_t| \leq \frac{M}{|x|^2} |u|, \] wi…
Momentum Ray Transforms, II: Range Characterization In the Schwartz space
Venkateswaran P. Krishnan, Ramesh Manna, Suman Kumar Sahoo +1
The momentum ray transform integrates a rank symmetric tensor field over lines of with the weight : $ (I^k\!f)(x,ξ)=\int_{-\infty}^\infty t^kłf(x+tξ),ξ^…
Carleman estimates for Baouendi-Grushin operators with applications to quantitative uniqueness and strong unique continuation
Agnid Banerjee, Nicola Garofalo, Ramesh Manna
In this paper we establish some new Carleman estimates for the Baouendi-Grushin operators , in (1.1) below. We apply such estimates to obtain: (i) an e…