COMPLEX ANALYSIS AND GEOMETRIA IN BANACH SPACES

Operation co-funded by EU cohesion policy (European Regional Development Fund (ERDF)) under the programme Multi-regional Spain - ERDF (2014ES16RFOP002), managing authority: Subdirección General de Gestión del FEDER, de la Dirección General de Fondos Europeos del Ministerio de Hacienda.. The source names no beneficiary for this operation. Location: Valencia Province (NUTS ES523); Spain. Budget: total eligible expenditure EUR 69,575; EU co-financing EUR 34,787.5 (co-financing rate 50%), as stated by the source. Runs 2018-01-01 to 2022-09-30. Source: Kohesio, EU cohesion policy projects managed by national and regional authorities (not CORDIS); selected because its summary names quantum technology. Summary from Kohesio (English machine translation by the source): AS THE TITLE SAYS THIS SUBPROJECT HAS TWO MASTER RESEARCH LINES. ONE OF THEM IS ABOUT COMPLEX ANALYSIS IN FINITE AND INFINITE DIMENSIONS AND THE OTHER ONE IS LINEAR AND NONLINEAR GEOMETRY IN BANACH SPACES. CONCERNING THE COMPLEX ANALYSIS IN FINITE AND INFINITE DIMENSIONS LINE WE SHALL DEAL WITH THE FOLLOWING TOPICS OF RESEARCH: (A) DIRICHLET SERIES OF SEVERAL COMPLEX VARIABLES, WITH AN AMBITIOUS PROJECT OF EXTENDING OUR PREVIOUS RESULTS ABOUT ONE COMPLEX VARIABLE AND CONNECTING WITH HARMONIC ANALYSIS AND COMPLEX ANALYSIS IN FINITE AND INFINITE DIMENSION, AND THE QUANTUM FIELD THEORY. OUR MAIN OBJECTIVES IN THIS STUDY WILL BE TO INTRODUCE ANALOGOUS SPACES TO H_\INFTY FOR DIRICHLET SERIES OF SEVERAL COMPLEX VARIABLES AND TRY TO PROVE THAT THESE SPACES ARE BANACH ALGEBRAS. THEN WE WILL STUDY POSSIBLE ISOMETRIES BETWEEN THESE SPACES AND THE CORRESPONDING SPACES OF HOLOMORPHIC FUNCTIONS IN INFINITELY MANY VARIABLES AS WELL AS THE ISOMETRIES BETWEEN THESE SPACES AND OTHER SPACES OF DIRICHLET SERIES. ALSO WE ARE INTERESTED IN STUDYING THE POSSIBILITY OF THE EXISTENCE OF ISOMETRIES BETWEEN ANALOGOUS SPACES TO H_\INFTY OF DIFFERENT DIMENSIONS. FINALLY, WE WANT TO DEFINE AND STUDY OTHER TYPE OF SPACES OF MULTIPLE DIRICHLET SERIES ANALOGOUS TO THE HARDY SPACE HP. (B) BANACH ALGEBRAS AND SPACES OF POLYNOMIALS, WHERE WE WILL STUDY NEW OPEN PROBLEMS ABOUT THE SPACE OF MAXIMAL IDEALS OF BANACH ALGEBRAS OF HOLOMORPHIC FUNCTIONS AND POLYNOMIALS DEFINE ON COMPLEX BANACH SPACES. FOR EXAMPLE, ONE OF OUR OBJECTIVES WILL BE TO PROVE WHETHER THE ¿CLUSTER THEOREM¿ HOLDS FOR THE SPACE OF MAXIMAL IDEALS OF THE ALGEBRA OF THE BALL OF A BANACH SPACE. WE HAVE PROVED THE CASE L_2. WE ALSO WANT TO STUDY THE GLEASON PARTS OF THESE SPACES. IN THE GEOMETRY OF BANACH SPACES OUR MAIN OBJECTIVE IS THE BISHOP-PHELPS-BOLLOBAS PROPERTY WHERE WE CONTINUE WITH OUR SUCCESSFUL AND COORDINATED LINE OF WORK. ALTHOUGH IN THIS LINE MANY RESEARCH PAPERS WERE PUBLISHED STIL THERE ARE MANY INTERESTING PROBLEMS AS [shortened; the full text is on the Kohesio page]

Original source.

Source: Kohesio (EU cohesion policy projects), European Commission, Directorate-General for Regional and Urban Policy (DG REGIO). Retrieved 2026-10-21. Licence: CC0 1.0 (Cohesion Open Data Platform, dataset 2014-2020 Kohesio projects). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: public domain dedication (CC0 1.0).

AI-assisted summary: The operation titled 'Complex Analysis and Geometria in Banach Spaces' is co-funded by the EU under the ERDF, with a budget of EUR 69,575, running from January 1, 2018, to September 30, 2022, in Valencia Province, Spain. It focuses on complex analysis and geometry in Banach spaces. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.