ORTHOGONALITY AND APPROXIMATION: THEORY AND APPLICATIONS IN MATHEMATICAL PHYSICS

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: Spain. Budget: total eligible expenditure EUR 35,695; EU co-financing EUR 17,847.5 (co-financing rate 50%), as stated by the source. Runs 2019-01-01 to 2021-12-31. 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): THE OBJECTIVE OF THIS RESEARCH PROJECT IS TO INVESTIGATE ANALYTICAL PROPERTIES OF ORTHOGONAL POLYNOMIALS WITH RESPECT TO VARIOUS ORTHOGONALITY MODELS, AND THEIR APPLICATIONS IN MATHEMATICAL PHYSICS (MODELS AND APPLICATIONS IN WHICH THE PROJECT¿S TEAMS HAVE AN AMPLE AND CREDITED EXPERIENCE). IN PARTICULAR: (A) BISPECTRALITY AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS AND THEIR CONNECTIONS WITH THE PHYSICAL PROBLEMS MODELED BY DIFFERENTIAL AND DIFFERENCE OPERATORS, THAT HAVE AS EIGENVALUES THESE ORTHOGONAL POLYNOMIALS (WHICH ALSO ALLOWS AN EXACT CALCULATION THE SPECTRUM AND EIGENFUNCTIONS OF THEIR ASSOCIATED QUANTUM-MECHANIC MODELS). WE WILL STUDY BOTH, THE CONTINUOUS AND THE DISCRETE VERSIONS, FOCUSING ON THE STUDY OF THE STRUCTURE OF THE ASSOCIATED ALGEBRAS. BISPECTRALITY PROBLEMS FOR DIFFERENCE OPERATORS HAVE AN ADDITIONAL INTEREST DUE TO THEIR EQUIVALENCE WITH DISCRETE ORTHOGONAL POLYNOMIALS VIA THE DUALITY OF THE CLASSICAL FAMILIES OF DISCRETE ORTHOGONAL POLYNOMIALS. (B) MATRIX ORTHOGONALITY AND ORTHOGONALITY IN SEVERAL VARIABLES, AND THEIR APPLICATIONS TO SIGNAL FILTERING, DISCRETE MARKOV CHAINS WHERE THE INTERACTIONS ARE NOT RESTRICTED TO THE CLOSEST NEIGHBORS, AND TO TIME AND BAND LIMITING PROBLEMS. (C) ORTHOGONALITY AND INTEGRABLE SYSTEMS; APPLICATIONS ARE BASED ON THE FACT THAT THE FLOW, PARAMETRIZED ON CONTINUOUS OR DISCRETE TIME, CORRESPONDS IN THESE SYSTEMS WITH ORTHOGONAL POLYNOMIALS WITH RESPECT TO MEASURES WHICH ARE PERTURBED ACCORDING TO THE TIME PARAMETERS. WE WILL FOCUS ON THE TIME VARIATION OF THESE ORTHOGONAL POLYNOMIALS, THEIR COEFFICIENTS, THE COEFFICIENTS OF THEIR RECURRENCE RELATIONS, AND THEIR CHRISTOFFEL-DARBOUX KERNELS, SINCE THEY GIVE RISE TO SOLUTIONS TO THESE NON-LINEAR INTEGRABLE EQUATIONS. IN THIS PROJECT WE WILL EXTEND THE CONNECTIONS WITH INTEGRABLE SYSTEMS TO MOST OF THE WIDE CLASS OF ORTHOGONAL POLYNOMIALS ALREADY MENTIONED, ENHANCING IN THIS WAY THE POTENTIAL FOR THEIR STUDY AND THEIR APPLICATIONS. (D) RATIONAL APPROXIMATION (MAINLY [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 project "Orthogonality and Approximation: Theory and Applications in Mathematical Physics" investigates analytical properties of orthogonal polynomials and their applications in mathematical physics. It is co-funded by the EU with a budget of EUR 35,695, running from 2019 to 2021 in Spain. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.