Objective
The Cauchy integral operator is the prototype example of a singular integral operator in the complex variable setting
and the fundamental object to be understood in the problem of characterization of removable sets for bounded analytic functions. By many different reasons, the study of this operator has always been confined to the setting of Lipschitz paths.
However, recent developments in a relatively new technique called time-frequence analysis suggests that the theory may be extended to more general paths.
Therefore, we propose the study of boundedness of Cauchy integral operator defined over paths that can be rougher than Lipschitz. We are particularly interested in the case when the derivative of the function defining the path belongs to a particular Lebesgue space.
For such purpose, we propose the use of time-frequency analysis and the use of variation norms.
Once boundedness in Lebesgue spaces is obtained, we will be able to establish new lower bounds for the analytic capacity of a compact set, which which is a quantitative measurement of the possibility of being removable.
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP7-PEOPLE-2010-RG
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Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
08193 Cerdanyola Del Valles
Spain
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.