4 papers
Mixed Grushin Heat Equations with Riesz-Potential Nonlinearities in Marcinkiewicz Spaces: Subcritical, Critical, and Supercritical Regimes
Aparajita Dasgupta, Uttam Kumar Dolai
We study the nonlinear evolution equation where is the nonnegative self adjoint realization of Grushin o…
Hartee-type heat equation associated to fractional anharmonic oscillator on weighted modulation spaces
Aparajita Dasgupta, Uttam Kumar Dolai
We study Hartree-type nonlinear heat equations associated with fractional generalised anharmonic oscillators \(A_{k,l}\) in weighted modulation spaces. We first derive Strichartz-t…
Phase-Space Analysis of generalised Fractional Anharmonic and Ornstein-Uhlenbeck Semigroups on Weighted Modulation Spaces
Aparajita Dasgupta, Uttam Kumar Dolai
We develop a phase-space framework for fractional generalised anharmonic oscillators and their heat semigroups on weighted modulation spaces. We consider operators of the form \[ \…
Local Dispersive and Strichartz estimates for the Schrödinger equation associated to the Ornstein-Uhlenbeck operator
Aparajita Dasgupta, Uttam Kumar Dolai, Cheng Luo +1
In this paper we study the linear and nonlinear Schrödinger equations associated with the Ornstein-Uhlenbeck (OU) operator endowed with the Gaussian measure. While classical Strich…