Advanced search
Start date
Betweenand

Global ultradifferentiable functions, complex analysis, and PDE's

Grant number: 18/02663-0
Support type:Research Grants - Visiting Researcher Grant - International
Duration: September 01, 2018 - October 31, 2018
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Gustavo Hoepfner
Grantee:Gustavo Hoepfner
Visiting researcher: Andrew Seth Raich
Visiting researcher institution: University of Arkansas, United States
Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

We want to study regularity of partial differential equations inthe space of global $L^q$ Gevrey functions, recently introduced in [Z. Adwan, G. Hoepfner, and A. Raich, Global Lq-Gevrey functions and their applications, J. Geom. Anal. 27 (2017), no. 3, 1874-1913.] and [G. Hoepfner and A. Raich, Global Lq Gevrey functions, Paley-Weiner theorems, and the FBI transform, to appear, Indiana Univ. Math. J.] and in a generalized and new function space called the space of global $L^q$ Denjoy-Carleman functions.We aim to develop a wedge approach similar to a celebrated Bony's theorem [J. M. Bony, Équivalence des diverses notions de spectre singulier analytique, Séminaire Goulaouic-Schwartz (1976/1977), E quations aux dérivées partielles et analysefonctionnelle, Exp.No.3, CentreMath., École Polytech., Palaiseau,1977.] and among other results, we will focus on three main topics. The first establishes the existence of boundary values of continuous functions on a wedge. Next, we borrow the FBI transform approach from [G. Hoepfner and A. Raich, Global Lq Gevrey functions, Paley-Weiner theorems, and the FBI transform, to appear, Indiana Univ. Math. J.] to define global wavefront sets and try to prove a relationship between the inclusion of a direction in the global wavefront set and the existence of boundary values of sums of weighted $L^p$ functions defined in wedges. The last is an classical application namely, the relationship between the global characteristic set of a partial differential operator $P$ and the microglobal wavefront sets of $u$ and $Pu$. We also want to investigate other relations with this $L^q$ Global Denjoy-Carleman functions such as: Hardy spaces properties and the Grusin operator. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
Articles published in other media outlets (0 total):
More itemsLess items
VEICULO: TITULO (DATA)
VEICULO: TITULO (DATA)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
HOEPFNER, GUSTAVO; RAICH, ANDREW. Microglobal regularity and the global wavefront set. MATHEMATISCHE ZEITSCHRIFT, v. 291, n. 3-4, p. 971-998, . (17/06993-2, 17/03825-1, 18/02663-0)
COACALLE, JOEL; RAICH, ANDREW. Closed Range Estimates for (partial derivative)over-bar(b) on CR Manifolds of Hypersurface Type. JOURNAL OF GEOMETRIC ANALYSIS, v. 31, n. 1, p. 366-394, . (18/02663-0)

Please report errors in scientific publications list by writing to: cdi@fapesp.br.