Objective
The goal of the proposed two year project is to develop a general Banish space theory of time-frequency localized, redundant and stable non-orthogonal expansions (briefly Banish frames) and to study adaptive numerical schemes for (certain) linear (pseudo-differential) operator equations using their matrix representations with respect to such well-localized frames. Whereas the construction of unconditional (rasp. Rises) bases is no problem in the wavelet or Gabon analysis case (due to the group structure in the background) the extra flexibility in the construction of Banish frames is expected to be crucial when one tries to define such Banish frames overbore complex geometries like manifolds. Starting from the known cases of Banish frames of Gabon and wavelet type we want to investigate an intermediate time-frequency localizing family of Banish frames (flexible Wavelet-wavelet frames) generated by a parametric combination of modulations, translations and dilations (parameterised by alpha in [0,1]), applied to some given analysing function (or atom), and use size andsummability conditions on the corresponding coefficients in order to define so called alpha-modulation spaces. This achievement could be interpreted as a generalization of the atomic decomposition and co orbit space theory developed by Hechinger and Grouching around 1990. In fact, for the limiting cases alpha = 0 and alpha = these spaces coincide with modulation rasp. Besot spaces, whose Wavelet- rasp. Wavelet decompositions are characterized by suitable weighted mixed-norm sequence space. A bounded linear operator can be discredited by means of the representation with respect to a time-frequency localizing Banish frame. This gives rise to an equivalent singular (infinite) matrix representation of the operator whose a pseudo-inverse can be efficiently calculated e.g. by means of numerical adaptive schemes based on damped-Richardson iterative algorithm.
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.
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Keywords
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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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.
FP6-2002-MOBILITY-5
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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
WIEN
Austria
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