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Recensione a Catalogo dei manoscritti della Biblioteca Vallicelliana. Vol. II (Mss. lettera A), di V. d'Urso e P. Formica, con la revisione editoriale di L. Signorello
No full textPrime considerazioni su manoscritti e copisti a Napoli in epoca angioina e aragonese (1266-1494)
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Produzione, fruizione e circolazione meridionale dei manoscritti della Commedia (secc. XIV-XV). Per un apporto paleografico
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Anonymous Collaborators of Nikolaos Choniates’ atelier in Manuscripts from Achilles Statius’ Library
No full textLinear Schrödinger equation with an almost periodic potential
Full text linkWe study the reducibility of a linear Schrodinger equation subject to a small unbounded almost periodic perturbation which is analytic in time and space. Under appropriate assumptions on the smallness, analyticity, and on the frequency of the almost periodic perturbation, we prove that such an equation is reducible to constant coefficients via an analytic almost periodic change of variables. This implies control of both Sobolev and analytic norms for the solution of the corresponding Schrödinger equation for all times
Quadratic lifespan and growth of Sobolev norms for derivative Schrödinger equations on generic tori
Full text linkWe consider a family of Schrödinger equations with unbounded Hamiltonian quadratic nonlinearities on a generic tori of dimension d≥1. We study the behavior of high Sobolev norms Hs, s≫1, of solutions with initial conditions in Hs whose Hρ-Sobolev norm, 1≪ρ≪s, is smaller than ε≪1. We provide a control of the Hs-norm over a time interval of order O(ε−2). Due to the lack of conserved quantities controlling high Sobolev norms, the key ingredient of the proof is the construction of a modified energy equivalent to the “low norm” Hρ (when ρ is sufficiently high) over a nontrivial time interval O(ε−2). This is achieved by means of normal form techniques for quasi-linear equations involving para-differential calculus. The main difficulty is to control the possible loss of derivatives due to the small divisors arising form three waves interactions. By performing “tame” energy estimates we obtain upper bounds for higher Sobolev norms Hs
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