https://mathematicalanalysis.unibo.it/issue/feedBruno Pini Mathematical Analysis Seminar2017-02-10T16:11:44+01:00Annamaria Montanariannamaria.montanari@unibo.itOpen Journal Systems<strong>Bruno Pini Mathematical Analysis Seminar (BPMAS) – ISSN 2240-2829</strong> publishes seminars solicited by the Department of Mathematics, University of Bologna. It features recent developments in mathematical analysis.https://mathematicalanalysis.unibo.it/article/view/6685Some Remarks on Harmonic Projection Operators on Spheres2017-02-10T16:11:44+01:00Valentina Casarinovalentina.casarino@unipd.it<p>We give a survey of recent works concerning the mapping properties of joint harmonic projection operators, mapping the space of square integrable functions on complex and quaternionic spheres onto the eigenspaces of the Laplace-Beltrami operator and of a suitably defined subLaplacian. In particular, we discuss similarities and differences between the real, the complex and the quaternionic framework.</p>2017-02-10T16:04:54+01:00Copyright (c) 2016 Valentina Casarinohttps://mathematicalanalysis.unibo.it/article/view/6686Semiclassical Analysis in Infinite Dimensions: Wigner Measures2017-02-10T16:06:11+01:00Marco Falconimfalconi@mat.uniroma3.itWe review some aspects of semiclassical analysis for systems whose phase space is of arbitrary (possibly infinite) dimension. An emphasis will be put on a general derivation of the so-called Wigner classical measures as the limit of states in a noncommutative algebra of quantum observables.2017-02-10T16:04:55+01:00Copyright (c) 2016 Marco Falconihttps://mathematicalanalysis.unibo.it/article/view/6689Noncommutative Fourier Analysis on Invariant Subspaces: Frames of Unitary Orbits and Hilbert Modules over Group von Neumann Algebras2017-02-10T16:06:12+01:00Davide Barbieridavide.barbieri@uam.es<p>This is a joint work with E. Hernández, J. Parcet and V. Paternostro. We will discuss the structure of bases and frames of unitary orbits of discrete groups in invariant subspaces of separable Hilbert spaces. These invariant spaces can be characterized, by means of Fourier intertwining operators, as modules whose rings of coefficients are given by the group von Neumann algebra, endowed with an unbounded operator valued pairing which defines a noncommutative Hilbert structure. Frames and bases obtained by countable families of orbits have noncommutative counterparts in these Hilbert modules, given by countable families of operators satisfying generalized reproducing conditions. These results extend key notions of Fourier and wavelet analysis to general unitary actions of discrete groups, such as crystallographic transformations on the Euclidean plane or discrete Heisenberg groups.</p>2017-02-10T16:04:55+01:00Copyright (c) 2016 Davide Barbierihttps://mathematicalanalysis.unibo.it/article/view/6690Analytic Hypoellipticity and the Treves Conjecture2017-02-10T16:06:13+01:00Marco Mughettimarco.mughetti@unibo.itWe are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata in the Poisson-Treves stratification are symplectic. We discuss a model operator, <em>P</em>, (firstly appeared and studied in [3]) having a single symplectic stratum and prove that it is not analytic hypoelliptic. This yields a counterexample to the sufficient part of Treves conjecture; the necessary part is still an open problem.2017-02-10T16:04:56+01:00Copyright (c) 2016 Marco Mughettihttps://mathematicalanalysis.unibo.it/article/view/6691An Eigenvalue Problem for Nonlocal Equations2017-02-10T16:06:14+01:00Giovanni Molica Biscigmolica@unirc.itRaffaella Servadeiraffaella.servadei@uniurb.it<p>In this paper we study the existence of a positive weak solution for a class of nonlocal equations under Dirichlet boundary conditions and involving the regional fractional Laplacian operator...Our result extends to the fractional setting some theorems obtained recently for ordinary and classical elliptic equations, as well as some characterization properties proved for differential problems involving different elliptic operators. With respect to these cases studied in literature, the nonlocal one considered here presents some additional difficulties, so that a careful analysis of the fractional spaces involved is necessary, as well as some nonlocal L^q estimates, recently proved in the nonlocal framework.</p>2017-02-10T16:04:57+01:00Copyright (c) 2016 Giovanni Molica Bisci, Raffaella Servadeihttps://mathematicalanalysis.unibo.it/article/view/6692A Measure Zero UDS in the Heisenberg Group2017-02-10T16:06:15+01:00Andrea Pinamontiandrea.pinamonti@gmail.comGareth Speightgareth.speight@uc.edu<p>We show that the Heisenberg group contains a measure zero set N such that every real-valued Lipschitz function is Pansu differentiable at a point of N.</p>2017-02-10T16:04:57+01:00Copyright (c) 2016 Andrea Pinamonti, Gareth Speighthttps://mathematicalanalysis.unibo.it/article/view/6693Steiner Formula and Gaussian Curvature in the Heisenberg Group2017-02-10T16:06:16+01:00Eugenio Vecchieugenio.vecchi2@unibo.it<p>The classical Steiner formula expresses the volume of the ∈-neighborhood Ω<sub>∈ </sub>of a bounded and regular domain Ω⊂R<sup>n</sup> as a polynomial of degree n in ∈. In particular, the coefficients of this polynomial are the integrals of functions of the curvatures of the boundary ∂Ω. The aim of this note is to present the Heisenberg counterpart of this result. The original motivation for studying this kind of extension is to try to identify a suitable candidate for the notion of horizontal Gaussian curvature. The results presented in this note are contained in the paper [4] written in collaboration with Zoltàn Balogh, Fausto Ferrari, Bruno Franchi and Kevin Wildrick</p>2017-02-10T16:04:58+01:00Copyright (c) 2016 Eugenio Vecchihttps://mathematicalanalysis.unibo.it/article/view/6694On the First Boundary Value Problem for Hypoelliptic Evolution Equations: Perron-Wiener Solutions and Cone-Type Criteria2017-02-10T16:06:17+01:00Alessia E. Kogojakogoj@unisa.it<p>For every bounded open set Ω in R<sup>N</sup><sup>+1</sup>, we study the first boundary problem for a wide class of hypoelliptic evolution operators. The operators are assumed to be endowed with a well behaved global fundamental solution that allows us to construct a generalized solution in the sense of Perron-Wiener of the Dirichlet problem. Then, we give a criterion of regularity for boundary points in terms of the behavior, close to the point, of the fundamental solution of the involved operator. We deduce exterior conetype criteria for operators of Kolmogorov-Fokker-Planck-type, for the heat operators and more general evolution invariant operators on Lie groups. Our criteria extend and generalize the classical parabolic-cone condition for the classical heat operator due to Effros and Kazdan. The results presented are contained in [K16].</p>2017-02-10T16:04:58+01:00Copyright (c) 2016 Alessia E. Kogojhttps://mathematicalanalysis.unibo.it/article/view/6695Regularity Results for Local Minimizers of Functionals with Discontinuous Coefficients2017-02-10T16:06:18+01:00Raffaella Giovaraffaella.giova@uniparthenope.itAntonia Passarelli di Napoliantpassa@unina.it<p>We give an overview on recent regularity results of local vectorial minimizers of under two main features: the energy density is uniformly convex with respect to the gradient variable only at infinity and it depends on the spatial variable through a possibly discontinuous coefficient. More precisely, the results that we present tell that a suitable weak differentiability property of the integrand as function of the spatial variable implies the higher differentiability and the higher integrability of the gradient of the local minimizers. We also discuss the regularity of the local solutions of nonlinear elliptic equations under a fractional Sobolev assumption.</p>2017-02-10T16:04:59+01:00Copyright (c) 2016 Raffaella Giova, Antonia Passarelli di Napolihttps://mathematicalanalysis.unibo.it/article/view/6696Recent Progresses in the Theory of Nonlinear Nonlocal Problems2017-02-10T16:06:19+01:00Sunra Mosconimosconi@dmi.unict.itMarco Squassinamarco.squassina@unicatt.it<p>We overview some recent existence and regularity results in the theory of nonlocal nonlinear problems driven by the fractional p-Laplacian.</p>2017-02-10T16:05:00+01:00Copyright (c) 2016 Sunra Mosconi, Marco Squassinahttps://mathematicalanalysis.unibo.it/article/view/6697Linear Parabolic Mixed Problems in Spaces of Hölder Continuous Functions: Old and New Results2017-02-10T16:06:20+01:00Davide Guidettidavide.guidetti@unibo.it<p>We illustrate some old and new results, concerning linear parabolic mixed problems in spaces of Hölder continuous functions: we begin with the classical Dirichlet and oblique derivative problems and continue with dynamic and Wentzell boundary conditions.</p>2017-02-10T16:05:00+01:00Copyright (c) 2016 Davide Guidetti Guidettihttps://mathematicalanalysis.unibo.it/article/view/6698Identification for General Degenerate Problems of Hyperbolic Type2017-02-10T16:06:21+01:00Angelo Faviniangelo.favini@unibo.itGabriela Marinoschigabriela.marinoschi@acad.ro<p>A degenerate identification problem in Hilbert space is described, improving a previous paper [2]. An application to second order evolution equations of hyperbolic type is given. The abstract results are applied to concrete differential problems of interest in applied sciences.</p>2017-02-10T16:05:00+01:00Copyright (c) 2016 Angelo Favini, Gabriela Marinoschi