SISSA PreprintsThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.http://preprints.sissa.it:80/xmlui2019-12-10T15:54:35Z2019-12-10T15:54:35ZTwo-dimensional Schrödinger operators with point interactions: Threshold expansions, zero modes and Lp-boundedness of wave operatorsCornean, Horia D.Michelangeli, AlessandroYajima, Kenjihttp://preprints.sissa.it:8180/xmlui/handle/1963/353402019-10-10T23:20:28Z2019-10-10T00:00:00ZTwo-dimensional Schrödinger operators with point interactions: Threshold expansions, zero modes and Lp-boundedness of wave operators
Cornean, Horia D.; Michelangeli, Alessandro; Yajima, Kenji
Mathematics Subject Classiffcation 2010: 35P15, 35J10, 47A40, 81Q10
2019-10-10T00:00:00ZPeriodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional toriFonda, AlessandroKlun, GiulianoSfecci, Andreahttp://preprints.sissa.it:8180/xmlui/handle/1963/353392019-09-12T23:20:25Z2019-09-12T00:00:00ZPeriodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional tori
Fonda, Alessandro; Klun, Giuliano; Sfecci, Andrea
We prove the existence of periodic solutions of some infinite-dimensional nearly integrable
Hamiltonian systems, bifurcating from infinite-dimensional tori, by the use of a generalization
of the Poincaré–Birkhoff Theorem.
Dedicated to Shair Ahmad, on the occasion of his 85th birthday
2019-09-12T00:00:00ZConvergence of the conjugate gradient method with unbounded operatorsCaruso, NoeMichelangeli, Alessandrohttp://preprints.sissa.it:8180/xmlui/handle/1963/353382019-08-27T23:20:21Z2019-08-27T00:00:00ZConvergence of the conjugate gradient method with unbounded operators
Caruso, Noe; Michelangeli, Alessandro
In the framework of inverse linear problems on infinite-dimensional Hilbert space, we prove the convergence of the conjugate gradient iterates to an exact solution to the inverse problem in the most general case where the self-adjoint, non-negative operator is unbounded and with minimal, technically unavoidable assumptions on the initial guess of the iterative algorithm. The convergence is proved to always hold in the Hilbert space norm (error convergence), as well as at other levels of regularity (energy norm, residual, etc.) depending on the regularity of the iterates. We also discuss, both analytically and through a selection of numerical tests, the main features and differences of our Convergence result as compared to the case, already available in the literature, where the operator is bounded.
2019-08-27T00:00:00ZOn the blow-up of GSBV functions under suitable geometric properties of the jump setTasso, Emanuelehttp://preprints.sissa.it:8180/xmlui/handle/1963/353372019-11-08T00:20:26Z2019-06-01T00:00:00ZOn the blow-up of GSBV functions under suitable geometric properties of the jump set
Tasso, Emanuele
In this paper we investigate the fine properties of functions under suitable geometric conditions on the jump set. Precisely, given an open set Ω С Rn and given p > 1 we study the blow-up of functions u Є2 GSBV (Ω), whose jump sets belongs to an appropriate class Jp and whose approximate gradient is p-th power summable. In analogy with the theory of p-capacity in the context of Sobolev spaces, we prove that the blow-up of u converges up to a set of Hausdorff dimension less than or equal to n - p. Moreover, we are able to
prove the following result which in the case of W1,p (Ω) functions can be stated as follows: whenever uk strongly converges to u, then up to subsequences, uk pointwise converges to u except on a set whose Hausdorff dimension is at most n - p.
2019-06-01T00:00:00Z