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Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness

BHIMANI, DIVYANG G.; Manna, Ramesh; Nicola, Fabio; Thangavelu, Sundaram; Trapass, S. Ivan (Elsevier B.V., 2021-12)

We study the Hermite operator in and its fractional powers , in phase space. Namely, we represent functions f via the so-called short-time Fourier, alias Fourier-Wigner or Bargmann transform (g being a fixed window function), ...
On heat equations associated with fractional harmonic oscillators

BHIMANI, DIVYANG G.; Manna, Ramesh; Nicola, Fabio; Thangavelu, Sundaram; Trapasso, S. Ivan (Springer Nature, 2023-12)

We establish some fixed-time decay estimates in Lebesgue spaces for the fractional heat propagator e(-tH beta), t, beta > 0, associated with the harmonic oscillator H = -Delta+vertical bar x vertical bar(2). We then prove ...

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