Harmonic analysis on and geometry of fractal sets

Project Information

Grant agreement ID: FMBI982882

Start date

End date

Funded under

• Specific research and technological development programme in the field of the training and mobility of researchers, 1994-1998

Total cost No data

EU contribution No data

Coordinated by

National University of Ireland - Maynooth
Ireland

Objective

Research objectives and content
It is proposed to tackle problems in the area of intersection of geometric measure theory and harmonic analysis, focussing particularly on the interaction between geometric and analytic properties of sets. Proposed problems include: 1. providing a geometric characterization of general 1-dimensional subsets of the plane of analytic capacity zero, 2. investigating implications of L2-boundedness of various singular integral operators (in particular, discovering for which such operators L2-boundedness implies rectifiability), 3. discovering whether a set in the plane which has projections onto lines of positive length in almost every direction must have bounded Melnikov curvature, 4. understanding asymptotic doubling properties of general sets, 5. investigating relationships between Poincari and Trudinger inequalities, doubling or strong doubling conditions, and the geometry of sets.
Training content (objective, benefit and expected impact)
The proposed collaboration would strengthen the preexisting links between NUIM and the applicant's current institution, the University of Jyvdskyld. (The two departments are currently part of a network, and a number of members of staff collaborate regularly.) The applicant's previous training in geometric measure theory and real analysis, and the host's expertise in harmonic analysis, make collaboration on such problems very natural. The proposed project would also broaden the applicant's range of expertise, while building on her current research knowledge.
Links with industry / industrial relevance (22)
None.

Fields of science (EuroSciVoc)

CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.

• natural sciences › mathematics › pure mathematics › geometry

You need to log in or register to use this function

Programme(s)

• FP4-TMR - Specific research and technological development programme in the field of the training and mobility of researchers, 1994-1998

Topic(s)

• 0303 - Return grants

Call for proposal

Data not available

Funding Scheme

RGI - Research grants (individual fellowships)

Coordinator

National University of Ireland - Maynooth

• EU contribution: No data
• Address: 47 Maynooth, Co. Kildare ; Ireland
• Total cost: No data