Objective
The primary objective of this project is to make progress on central questions in Harmonic Analysis and related areas, notably Fourier restriction/extension theory and phase-space Analysis, through the lens of new phase-space representations involving the Wigner distribution.
Fourier restriction/extension theory — a driving force of modern Harmonic Analysis — aims to effectively control the constructive interference of bundles of travelling waves. Several physical phenomena are described in terms of Fourier extension operators. In simple terms, these objects convert input functions — associated to the initial data of a partial differential equation (PDE) — into bundles of plane waves travelling in different directions. The Schrödinger and Helmholtz equations are the most well-known examples of PDEs whose solutions are given by Fourier extension operators. The former describes how the wave function of a quantum system evolves, whereas the latter models, for instance, the behaviour of electromagnetic waves in confined spaces like optical fibres.
Energy maximisation is a modern challenge in Signal Processing and phase-space Analysis, with applications in medical imaging resolution, noise reduction in audio processing and seismology, to mention a few. An exciting link between Fourier extension operators and the problem of energy maximisation was recently discovered in my recent work via Flandrin's conjecture, which predicts that convex sets are efficient phase-space signal filters: isolating the phase-space content of a signal to a convex set via its Wigner distribution does not increase the signal's energy by too much.
By capitalising on the phase-space perspective provided by Wigner-type distributions, this highly intradisciplinary project aims to establish new results and connections in two interrelated programmes covering both areas described above.
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. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences physical sciences quantum physics
- natural sciences earth and related environmental sciences geology seismology
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
- engineering and technology medical engineering diagnostic imaging
- natural sciences physical sciences optics fibre optics
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
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.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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Topic(s)
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.
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.
Funding Scheme
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.
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.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2025-PF
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
28006 MADRID
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.