Research
Research interests:
Brascamp-Lieb and geometric type inequalities
Resonances of invariant differential operators on Lie groups and symmetric spaces
Spectral properties of differential operators in non-Euclidean settings
Harmonic analysis on symmetric spaces
Potential theory
Irregularities of point distributions
Publications:
R.B., M. Dalla Riva, P. Luzzini, P. Musolino, The Functional Analytic Approach for quasi-periodic boundary value problems for the Helmholtz equation, Adv. Differential Equations 29 (2024), no. 1/2, 27-68. (Preprint)
R.B., A note on a Capelli operator and its resonance, In: Ruzhansky, M., Van Bockstal, K. (eds) Extended Abstracts 2021/2022. APDEGS 2021. Trends in Mathematics(), vol 2. Birkhäuser, Cham.
R.B., A. Pasquale, T. Przebinda, The resonances of the Capelli operators for small split orthosymplectic dual pairs, J. Lie Theory 33 (2023), no.1, 93-132. (Preprint)
R.B., P. Ciatti, J. Green, J. Wright, Oscillating spectral multipliers on groups of Heisenberg type, Rev. Mat. Iberoam. 38 (2022), no. 5, 1529-1551. (Preprint)
R.B., A family of sharp inequalities on real spheres, Complex Var. Elliptic Equ. 67 (2022), no. 8, 2030-2042. (Preprint)
R.B., Brascamp-Lieb inequalities on Compact Homogeneous Spaces, Anal. Geom. Metr. Spaces 7 (2019), no. 1, 130–157.
R.B., V. Casarino, P. Ciatti, On the norms of quaternionic harmonic projection operators, C. R. Math. Acad. Sci. Paris 356 (2018), no. 5, 482–488.
Submitted papers:
R.B., M. Dalla Riva, B. Luczak, Continuous harmonic functions on a ball that are not in H^s for s>1/2. (Preprint)
R.B., M. Dalla Riva, P. Luzzini, P. Musolino, Periodic layer potentials and domain perturbations. (Preprint)
Academic works:
Ph.D. Thesis: Geometric integral inequalities on homogeneous spaces
Other publications:
R.B., Brascamp-Lieb inequalities and heat-flow monotonicity, Seminario Dottorato 2017/18, Università degli Studi di Padova, 117-127.