CAUCHY INTEGRAL

The Cauchy integral operator over general paths

 Coordinatore UNIVERSITAT AUTONOMA DE BARCELONA 

 Organization address address: Campus UAB -BELLATERRA- s/n
city: CERDANYOLA DEL VALLES
postcode: 8193

contact info
Titolo: Ms.
Nome: Queralt
Cognome: Gonzalez Matos
Email: send email
Telefono: +34 93 581 2854
Fax: +34 93 581 2023

 Nazionalità Coordinatore Spain [ES]
 Totale costo 45˙000 €
 EC contributo 45˙000 €
 Programma FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
 Code Call FP7-PEOPLE-2010-RG
 Funding Scheme MC-ERG
 Anno di inizio 0
 Periodo (anno-mese-giorno) 0000-00-00   -   0000-00-00

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    UNIVERSITAT AUTONOMA DE BARCELONA

 Organization address address: Campus UAB -BELLATERRA- s/n
city: CERDANYOLA DEL VALLES
postcode: 8193

contact info
Titolo: Ms.
Nome: Queralt
Cognome: Gonzalez Matos
Email: send email
Telefono: +34 93 581 2854
Fax: +34 93 581 2023

ES (CERDANYOLA DEL VALLES) coordinator 45˙000.00

Mappa


 Word cloud

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paths    integral    cauchy    analytic    boundedness    lipschitz    removable    time    operator    lebesgue    setting   

 Obiettivo del progetto (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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