R. Bramati

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20192026

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math.AP2022

The Functional Analytic Approach for quasi-periodic boundary value problems for the Helmholtz equation

Roberto Bramati, Matteo Dalla Riva, Paolo Luzzini +1

We lay down the preliminary work to apply the Functional Analytic Approach to quasi-periodic boundary value problems for the Helmholtz equation. This consists in introducing a quas…

math.RT2022

The resonances of the Capelli operators for small split orthosymplectic dual pairs

Roberto Bramati, Angela Pasquale, Tomasz Przebinda

Let $(G, G^{'})$ be a reductive dual pair in $S p (W)$ with rank $G \leq$ rank $G^{'}$ and $G^{'}$ semisimple. The image of the Casimir element of the universal enveloping algebra of $G^{'}$ under…

math.AP2022

Continuous harmonic functions on a ball that are not in $H^{s}$ for $s > 1/2$

Roberto Bramati, Matteo Dalla Riva, Brian Luczak

We show that there are harmonic functions on a ball $B_{n}$ of $R^{n}$ , $n \geq 2$ , that are continuous up to the boundary (and even Hölder continuous) but not in the…

The Functional Analytic Approach for quasi-periodic boundary value problems for the Helmholtz equation

The resonances of the Capelli operators for small split orthosymplectic dual pairs

Continuous harmonic functions on a ball that are not in Hs for s>1/2

Continuous harmonic functions on a ball that are not in $H^{s}$ for $s > 1/2$