Activities and Results



It was proved that a Stein space that admits a bounded plurisubharmonic exhaustion, not necessarily continuous, is hyperconvex.
It was given an example of a bounded Stein domain in, the n-dimensional affine complex space with smooth boundary, which is not Runge and whose intersection with every complex line is simply connected.
It was solved the Levi problem for unbranched Riemann domains over Stein spaces with isolated singularities.
Based on the concept of mass transportation, it was introduced and studied a notion of rough curvature bound for the Ricci curvature on discrete metric spaces.
It was proved that the Laplace transform establishes a bijection between a class of resolvents and a class of semi-groups acting on an abstract ordered convex cone.
It was computed the resolvent of a semi-group of positive, nonlinear operators acting on measures. It has been shown that this resolvent has a natural extension to a larger set of measures (not necessarily positive), it was given a characterization for this type of resolvent in terms of the infinitesimal generator, there were described the invariant and excessive elements with respect to the resolvent/the sub-group.
We extended in the one- and multi-dimensional case some results from the relaxed variational calculus which are based on L1-boundedness conditions for minimizing sequences.
There were obtained sufficient conditions for a transformation f(z,t) to be an alpha-prestarlike subordination chain on (0,1], extending in this way a result of S. Ruscheweyh.
We studied the notion of convex subordination chain for transformations of several complex variables.
We extended and generalized classical results in the theory of differential subordination and superordination.
We studied the properties of two integral operators on the classes of functions M(beta) and N(beta).
We extended the maximum principle to a class non-analytic functions defined on the unit disc in the complex plane.
We obtained a Schwarz Lemma for a class non-analytic functions defined on the unit disc in the complex plane.
Using the differential subordination method we derived several properties of some differential subordinations which were obtained using certain generalized differential operators



Papers - published or accepted

  • Viorel Vajaitu: "Stein spaces with plurisubharmonic bounded exhaustion functions"
    - Mathematische Annalen, 336, no. 3, November 2006

  • Cezar Joita: "On a problem of Bremermann concerning Runge domains"
    - Mathematische Annalen, 337, no. 2, February 2007

  • Mihnea Coltoiu, Klas Diederich: " The Levi problem for Riemann domains over Stein spaces with isolated singularities"
    - to appear in Mathematische Annalen

  • Eugen Popa: "A Hille--Yosida type theorem in ordered convex cones",
    - Positivity, Volume 10, Number 3, September, 2006,

  • Liviu Florescu, C. Godet-Thobie: "A version of Biting Lemma for unbounded sequences in L1_E with applications"
    - AIP Conf. Proc. 835 (2006),

  • Eugen Popa: "Some remarks on semigroups acting on positive measures",
    - to appear in Proceedings of the International Conference on Applied Analysis and Differential Equations, Iasi 4 - 9 sept. 2006.

  • Gabriela Kohr, Petru T. Mocanu, I. Serb: "Convex and alpha-prestarlike subordination chains"
    - to appear in J. Math. Anal. Appl.

  • M.E. Gageonea, M.N. Pascu, N.R. Pascu: "A maximum modulus principle for a class of non-analytic functions defined in the unit disk"
    - to appear in Mathematica (Cluj)

  • M.E. Gageonea, M.N. Pascu, N.R. Pascu: "A Schwarz lemma for non-analytic functions defined in the unit disk"
    - to appear in Mathematica (Cluj)

  • Mihai Cristea: "Mappings of finite distortion: Zoric's theorem, equicontinuity results"
    - to appear in Rev. Roumaine Math. Pures Appl




    Preprints

  • Anca Bonciocat, Karl-Theodor Sturm: "Mass transportation and rough curvature bounds for discrete spaces"

  • Liviu Florescu: "Finite tight sets"

  • Liviu Florescu: "Rezultate de existenta relaxata Ón Calculul Variational"

  • Marian Pantiruc: "Transformata Fourier asupra semigrupului asociat Laplaceanului pe grupul Heisenberg"

  • I. Graham, H. Hamada, G. Kohr: "Convex subordination chains in several complex variables"

  • T. Bulboaca: "Sandwich-type theorems for a class of integral operators"

  • D. Breaz: "Certain integral operators on the classes M(beta) and N(beta)"

  • G.I. Oros, G. Oros: "Differential subordinations obtained by using generalized Salagean and Ruscheweyh operators"



    Conference and Seminar Presentation

  • Lucian Beznea: "Markov processes associated with Lp-resolvents: application to the quasi-regular Dirichlet forms", invited speaker, One Day Workshop on Stochastic Analysis, Bielefeld, Germania, August 16, 2006.
  • Lucian Beznea: "Markov processes associated with Lp-resolvents and applications to stochastic differential equations on Hilbert space", invited speaker, Stochastic Analysis and Applications-RIMS Workshops, Kyoto, Japonia, September 11-15, 2006.
  • Eugen Mihailescu: "Metric properties of some dynamically constructed sets", invited talk, Paris 11 University(Orsay)
  • Mihnea Coltoiu: "Recent results concerning the Levi problem on singular spaces", Scuola Normale Superiore di Pisa, October 2006
  • Cezar Joita: "On some notions of convexity", Humboldt University, Berlin, December 2006
  • Eugen Popa: "Some remarks on semigroups acting on positive measures", International Conference on Applied Analysis and Differential Equations, Iasi September 4 - 9, 2006.
  • Grigore Stefan Salagean: "Subordinations Differentielles", 8ieme Colloque Franco-Roumaine de Mathematiques Appliques, Chambery, Franta, 28 August - 1 September, 2006.
  • Eugen Popa: "Some remarks on a non-linear semigroup acting on positive measures", Potential Analysis IMAR Workshop, October 3 - 4, 2006, Bucuresti.
  • Eugen Popa: "O caracterizare pentru un semigrup de operatori neliniari pe masuri pozitive", Sesiunea de comunicari stiintifice a Facultatii de Matematica, Zilele Universitatii "Al. I. Cuza" Iasi, October 2006.
  • Liviu Florescu: "Multimi Jordan asimptotic marginite si rezultate de compacitate Ón "W1,1 (Omega), Sesiunea de comunicari stiintifice a Facultatii de Matematica, Iasi, October 27-28, 2006.
  • Marian Pantiruc: "Transformata Fourier asupra semigrupului asociat Laplaceanului pe grupul Heisenberg", Sesiunea de comunicari stiintifice a Facultatii de Matematica, Zilele Universitatii "Al. I. Cuza" Iasi, October 2006.