Bruno Pini Mathematical Analysis Seminar
https://mathematicalanalysis.unibo.it/
<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.Dipartimento di Matematica, Università di Bolognaen-USBruno Pini Mathematical Analysis Seminar2240-2829<p>Copyrights and publishing rights of all the texts on this journal belong to the respective authors without restrictions.</p><div><a href="http://creativecommons.org/licenses/by/3.0/" rel="license"><img src="https://i.creativecommons.org/l/by/3.0/88x31.png" alt="Creative Commons License" /></a></div><p>This journal is licensed under a <a href="http://creativecommons.org/licenses/by/3.0/" rel="license">Creative Commons Attribution 3.0 Unported License</a>. (<a href="http://creativecommons.org/licenses/by/3.0/legalcode">full legal code</a>) <br />See also our <a href="/about/editorialPolicies#openAccessPolicy">Open Access Policy</a>.</p>Some Remarks on Harmonic Projection Operators on Spheres
https://mathematicalanalysis.unibo.it/article/view/6685
<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>Valentina Casarino
Copyright (c) 2016 Valentina Casarino
http://creativecommons.org/licenses/by/3.0
2017-02-102017-02-107111710.6092/issn.2240-2829/6685Semiclassical Analysis in Infinite Dimensions: Wigner Measures
https://mathematicalanalysis.unibo.it/article/view/6686
We 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.Marco Falconi
Copyright (c) 2016 Marco Falconi
http://creativecommons.org/licenses/by/3.0
2017-02-102017-02-1071183510.6092/issn.2240-2829/6686Noncommutative Fourier Analysis on Invariant Subspaces: Frames of Unitary Orbits and Hilbert Modules over Group von Neumann Algebras
https://mathematicalanalysis.unibo.it/article/view/6689
<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>Davide Barbieri
Copyright (c) 2016 Davide Barbieri
http://creativecommons.org/licenses/by/3.0
2017-02-102017-02-1071365210.6092/issn.2240-2829/6689Analytic Hypoellipticity and the Treves Conjecture
https://mathematicalanalysis.unibo.it/article/view/6690
We 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.Marco Mughetti
Copyright (c) 2016 Marco Mughetti
http://creativecommons.org/licenses/by/3.0
2017-02-102017-02-1071536810.6092/issn.2240-2829/6690An Eigenvalue Problem for Nonlocal Equations
https://mathematicalanalysis.unibo.it/article/view/6691
<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>Giovanni Molica BisciRaffaella Servadei
Copyright (c) 2016 Giovanni Molica Bisci, Raffaella Servadei
http://creativecommons.org/licenses/by/3.0
2017-02-102017-02-1071698410.6092/issn.2240-2829/6691A Measure Zero UDS in the Heisenberg Group
https://mathematicalanalysis.unibo.it/article/view/6692
<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>Andrea PinamontiGareth Speight
Copyright (c) 2016 Andrea Pinamonti, Gareth Speight
http://creativecommons.org/licenses/by/3.0
2017-02-102017-02-1071859610.6092/issn.2240-2829/6692Steiner Formula and Gaussian Curvature in the Heisenberg Group
https://mathematicalanalysis.unibo.it/article/view/6693
<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>Eugenio Vecchi
Copyright (c) 2016 Eugenio Vecchi
http://creativecommons.org/licenses/by/3.0
2017-02-102017-02-10719711510.6092/issn.2240-2829/6693On the First Boundary Value Problem for Hypoelliptic Evolution Equations: Perron-Wiener Solutions and Cone-Type Criteria
https://mathematicalanalysis.unibo.it/article/view/6694
<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>Alessia E. Kogoj
Copyright (c) 2016 Alessia E. Kogoj
http://creativecommons.org/licenses/by/3.0
2017-02-102017-02-107111612810.6092/issn.2240-2829/6694Regularity Results for Local Minimizers of Functionals with Discontinuous Coefficients
https://mathematicalanalysis.unibo.it/article/view/6695
<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>Raffaella GiovaAntonia Passarelli di Napoli
Copyright (c) 2016 Raffaella Giova, Antonia Passarelli di Napoli
http://creativecommons.org/licenses/by/3.0
2017-02-102017-02-107112914610.6092/issn.2240-2829/6695Recent Progresses in the Theory of Nonlinear Nonlocal Problems
https://mathematicalanalysis.unibo.it/article/view/6696
<p>We overview some recent existence and regularity results in the theory of nonlocal nonlinear problems driven by the fractional p-Laplacian.</p>Sunra MosconiMarco Squassina
Copyright (c) 2016 Sunra Mosconi, Marco Squassina
http://creativecommons.org/licenses/by/3.0
2017-02-102017-02-107114716410.6092/issn.2240-2829/6696Linear Parabolic Mixed Problems in Spaces of Hölder Continuous Functions: Old and New Results
https://mathematicalanalysis.unibo.it/article/view/6697
<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>Davide Guidetti
Copyright (c) 2016 Davide Guidetti Guidetti
http://creativecommons.org/licenses/by/3.0
2017-02-102017-02-107116517410.6092/issn.2240-2829/6697Identification for General Degenerate Problems of Hyperbolic Type
https://mathematicalanalysis.unibo.it/article/view/6698
<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>Angelo FaviniGabriela Marinoschi
Copyright (c) 2016 Angelo Favini, Gabriela Marinoschi
http://creativecommons.org/licenses/by/3.0
2017-02-102017-02-107117518810.6092/issn.2240-2829/6698