SISSA Open ScienceThe SISSA Open Science digital repository system captures, stores, indexes, preserves, and distributes digital research material.http://preprints.sissa.it:80/xmlui2021-03-06T07:59:14Z2021-03-06T07:59:14ZOn Dini derivatives of real functionsFonda, AlessandroKlun, GiulianoSfecci, Andreahttp://preprints.sissa.it:8180/xmlui/handle/1963/354262021-03-02T00:20:27Z2021-01-01T00:00:00ZOn Dini derivatives of real functions
Fonda, Alessandro; Klun, Giuliano; Sfecci, Andrea
For a continuous function f, the set Vf made of those points
where the lower left derivative is strictly less than the upper right derivative is totally disconnected. Besides continuity, alternative assumptions
are proposed so to preserve this property. On the other hand, we construct a function f whose set Vf coincides with the entire domain, and
nevertheless f is continuous on an infinite set, possibly having infinitely
many cluster points. Some open problems are proposed.
SISSA 9/2021/MATE
2021-01-01T00:00:00ZOn real resonances for three-dimensional Schrodinger operators with point ¨ interactions†Michelangeli, AlessandroScandone, Raffaelehttp://preprints.sissa.it:8180/xmlui/handle/1963/354252021-02-23T00:20:36Z2018-01-01T00:00:00ZOn real resonances for three-dimensional Schrodinger operators with point ¨ interactions†
Michelangeli, Alessandro; Scandone, Raffaele
We prove the absence of positive real resonances for Schrodinger operators with finitely ¨
many point interactions in R 3 and we discuss such a property from the perspective of dispersive and scattering features of the associated Schrodinger propagator.
SISSA preprint 40-2018-MATE
2018-01-01T00:00:00ZKrylov Solvability of Unbounded Inverse Linear ProblemsCaruso, Noè AngeloMichelangeli, Alessandrohttp://preprints.sissa.it:8180/xmlui/handle/1963/354242021-02-23T00:20:35Z2019-01-01T00:00:00ZKrylov Solvability of Unbounded Inverse Linear Problems
Caruso, Noè Angelo; Michelangeli, Alessandro
. The abstract issue of ‘Krylov solvability’ is extensively discussed for the inverse problem Af = g where A is a (possibly unbounded) linear operator on an infinite-dimensional Hilbert space, and
g is a datum in the range of A. The question consists of whether the
solution f can be approximated in the Hilbert norm by finite linear
combinations of g, Ag, A2g,... , and whether solutions of this sort exist
and are unique. After revisiting the known picture when A is bounded,
we study the general case of a densely defined and closed A. Intrinsic
operator-theoretic mechanisms are identified that guarantee or prevent
Krylov solvability, with new features arising due to the unboundedness.
Such mechanisms are checked in the self-adjoint case, where Krylov
solvability is also proved by conjugate-gradient-based techniques.
2019-01-01T00:00:00ZOn the theory of self-adjoint extensions of positive definite operatorsKhotyakov, M..Michelangeli, Alessandrohttp://preprints.sissa.it:8180/xmlui/handle/1963/354232021-02-23T00:20:34Z2015-01-01T00:00:00ZOn the theory of self-adjoint extensions of positive definite operators
Khotyakov, M..; Michelangeli, Alessandro
SISSA preprint 8/2015/MATE
2015-01-01T00:00:00Z