00971nas a2200145   4500008004100000245008600041210006900127300001100196490000700207520050000214100002900714700002100743700002300764856003800787       2018                        eng d00aFractional powers and singular perturbations of quantum differential Hamiltonians0 aFractional powers and singular perturbations of quantum differen  a0721060 v593 a<p>We consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.</p>1 aMichelangeli, Alessandro1 aOttolini, Andrea1 aScandone, Raffaele  uhttps://doi.org/10.1063/1.503385601226nas a2200193   4500008004100000022001400041245006800055210006500123300001600188490000800204520054000212653002300752653006700775653004400842100002300886700002900909700002300938856007100961       2018                        eng d  a0022-123600aOn fractional powers of singular perturbations of the Laplacian0 afractional powers of singular perturbations of the Laplacian  a1551 - 16020 v2753 a<p>We qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.</p>10aPoint interactions10aRegular and singular component of a point-interaction operator10aSingular perturbations of the Laplacian1 aGeorgiev, Vladimir1 aMichelangeli, Alessandro1 aScandone, Raffaele  uhttp://www.sciencedirect.com/science/article/pii/S002212361830104601281nas a2200121   4500008004100000245008200041210006900123520085300192100002001045700001701065700002901082856004801111       2017                        en  d00aFriedrichs systems in a Hilbert space framework: solvability and multiplicity0 aFriedrichs systems in a Hilbert space framework solvability and 3 aThe Friedrichs (1958) theory of positive symmetric systems of first order partial
differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antonić and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide suffcient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.1 aAntonić, Nenad1 aErceg, Marko1 aMichelangeli, Alessandro  uhttp://preprints.sissa.it/handle/1963/35280