TOPICS IN FOURIER ANALYSIS AND APPLICATIONS (Q3147615): Difference between revisions
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(Removed claim: summary (P836): THE PROPOSED RESEARCH PROJECT IS PART OF THE HARMONIC ANALYSIS. THIS FIELD OF STUDY CONNECTS WITH OTHER AREAS OF WORK, AMONG WHICH WE POINT OUT THE EQUATIONS IN PARTIAL DERIVATIVES, THE THEORY OF NUMBERS AND THE THEORY OF SIGNALS, WHERE THERE ARE NUMEROUS APPLICATIONS OF THE RESULTS OBTAINED IN THE CONTEXT OF THE HARMONIOUS ANALYSIS. IN SPAIN THIS BRANCH OF ANALYSIS OCCUPIES NUMEROUS RESEARCHERS, THERE ARE IN SEVERAL UNIVERSITIES WORKING GROUP...) |
(Created claim: summary (P836): THE PROPOSED RESEARCH PROJECT IS PART OF THE HARMONIC ANALYSIS. THIS FIELD OF STUDY CONNECTS WITH OTHER AREAS OF WORK, AMONG WHICH WE POINT OUT THE EQUATIONS IN PARTIAL DERIVATIVES, THE THEORY OF NUMBERS AND THE THEORY OF SIGNALS, WHERE THERE ARE NUMEROUS APPLICATIONS OF THE RESULTS OBTAINED IN THE CONTEXT OF THE HARMONIOUS ANALYSIS. IN SPAIN THIS BRANCH OF ANALYSIS OCCUPIES NUMEROUS RESEARCHERS, THERE ARE IN SEVERAL UNIVERSITIES WORKING GROUPS...) |
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THE PROPOSED RESEARCH PROJECT IS PART OF THE HARMONIC ANALYSIS. THIS FIELD OF STUDY CONNECTS WITH OTHER AREAS OF WORK, AMONG WHICH WE POINT OUT THE EQUATIONS IN PARTIAL DERIVATIVES, THE THEORY OF NUMBERS AND THE THEORY OF SIGNALS, WHERE THERE ARE NUMEROUS APPLICATIONS OF THE RESULTS OBTAINED IN THE CONTEXT OF THE HARMONIOUS ANALYSIS. IN SPAIN THIS BRANCH OF ANALYSIS OCCUPIES NUMEROUS RESEARCHERS, THERE ARE IN SEVERAL UNIVERSITIES WORKING GROUPS WITH GREAT INTERNATIONAL PRESTIGE. SIGNIFICANT RESULTS HAVE RECENTLY BEEN OBTAINED ON THE NARROWING OF OSCILLATION AND VARIANCE OPERATORS ASSOCIATED WITH OPERATORs’ FAMILIES (E.G. PARTIAL SUMS FOR FOURIER AND WALSH SERIES). WE INTEND TO ANALYSE OSCILLATION AND VARIATION OPERATORS IN DIFFERENT CONTEXTS: CONVERGENCE TO THE DATA IN THE SCHRODINGER EQUATION, ORTHOGONAL AND TRANSFORMED SERIES OF RIESZ FOR THE HEISENBERG GROUP. WE ALSO AIM TO STUDY CERTAIN CLASSES OF ANISOTROPIC SPACES, WHOSE ANISOTROPY IS DESCRIBED BY CONSTANT OR VARIABLE EXPANSIVE MATRICES. IN PARTICULAR, WE INTEND TO STUDY HARDY ANISOTROPIC SPACES WITH VARIABLE EXPONENT. THE HARMONIC ANALYSIS ASSOCIATED WITH ORTHOGONAL SYSTEMS AND SEMI-GROUPS OF OPERATORS HAS BEEN AN ACTIVE AREA OF WORK IN THE LAST DECADE. IN RELATION TO THIS TOPIC WE PROPOSE TO ADDRESS DIFFERENT ISSUES (INDEPENDENT ESTIMATES OF DIMENSION, WEIGHTS, HARDY SPACES,) IN THE CONTEXTS OF LAGUERRE AND BESSEL. IN ADDITION, WE WILL STUDY BANACH MULTIVARIATE LITTLEWOOD-PALEY FUNCTIONS VALUED USING -RADONIFYING OPERATORS, IN ORDER TO OBTAIN CONDITIONS THAT GUARANTEE THE BOUNDING (IN DIFFERENT SPACES) OF MULTIVARIATE MULTIVARIATE MULTIPLIERS DEFINED FOR HERMITE AND LAGUERRE SERIES. THESE RESULTS ON MULTIPLIERS WILL ALLOW US TO CHARACTERISE SOBOLEV BANACH-VALUED SPACES IN THESE CONTEXTS. ON THE OTHER HAND, WE ALSO AIM TO STUDY DIFFERENT ISSUES (ACCOMMODATION AND COMPACTNESS OF OPERATORS, CARLESON MEASUREMENTS,) IN RELATION TO GENERALISED FOCK SPACES ASSOCIATED WITH ORTHOGONAL SYSTEMS, AND WITH Q_ SPACES. IN ADDITION, WE INTEND TO STUDY THE CHARACTERISATIONS USING BRUSHLETS OF VALUED HARDY AND BMO BANACH SPACES AND, USING MEASUREMENTS OF INCOMPACITY, WHEN CERTAIN SINGULAR INTEGRAL OPERATORS ARE COMPACT. (English) | |||||||||||||||
| Property / summary: THE PROPOSED RESEARCH PROJECT IS PART OF THE HARMONIC ANALYSIS. THIS FIELD OF STUDY CONNECTS WITH OTHER AREAS OF WORK, AMONG WHICH WE POINT OUT THE EQUATIONS IN PARTIAL DERIVATIVES, THE THEORY OF NUMBERS AND THE THEORY OF SIGNALS, WHERE THERE ARE NUMEROUS APPLICATIONS OF THE RESULTS OBTAINED IN THE CONTEXT OF THE HARMONIOUS ANALYSIS. IN SPAIN THIS BRANCH OF ANALYSIS OCCUPIES NUMEROUS RESEARCHERS, THERE ARE IN SEVERAL UNIVERSITIES WORKING GROUPS WITH GREAT INTERNATIONAL PRESTIGE. SIGNIFICANT RESULTS HAVE RECENTLY BEEN OBTAINED ON THE NARROWING OF OSCILLATION AND VARIANCE OPERATORS ASSOCIATED WITH OPERATORs’ FAMILIES (E.G. PARTIAL SUMS FOR FOURIER AND WALSH SERIES). WE INTEND TO ANALYSE OSCILLATION AND VARIATION OPERATORS IN DIFFERENT CONTEXTS: CONVERGENCE TO THE DATA IN THE SCHRODINGER EQUATION, ORTHOGONAL AND TRANSFORMED SERIES OF RIESZ FOR THE HEISENBERG GROUP. WE ALSO AIM TO STUDY CERTAIN CLASSES OF ANISOTROPIC SPACES, WHOSE ANISOTROPY IS DESCRIBED BY CONSTANT OR VARIABLE EXPANSIVE MATRICES. IN PARTICULAR, WE INTEND TO STUDY HARDY ANISOTROPIC SPACES WITH VARIABLE EXPONENT. THE HARMONIC ANALYSIS ASSOCIATED WITH ORTHOGONAL SYSTEMS AND SEMI-GROUPS OF OPERATORS HAS BEEN AN ACTIVE AREA OF WORK IN THE LAST DECADE. IN RELATION TO THIS TOPIC WE PROPOSE TO ADDRESS DIFFERENT ISSUES (INDEPENDENT ESTIMATES OF DIMENSION, WEIGHTS, HARDY SPACES,) IN THE CONTEXTS OF LAGUERRE AND BESSEL. IN ADDITION, WE WILL STUDY BANACH MULTIVARIATE LITTLEWOOD-PALEY FUNCTIONS VALUED USING -RADONIFYING OPERATORS, IN ORDER TO OBTAIN CONDITIONS THAT GUARANTEE THE BOUNDING (IN DIFFERENT SPACES) OF MULTIVARIATE MULTIVARIATE MULTIPLIERS DEFINED FOR HERMITE AND LAGUERRE SERIES. THESE RESULTS ON MULTIPLIERS WILL ALLOW US TO CHARACTERISE SOBOLEV BANACH-VALUED SPACES IN THESE CONTEXTS. ON THE OTHER HAND, WE ALSO AIM TO STUDY DIFFERENT ISSUES (ACCOMMODATION AND COMPACTNESS OF OPERATORS, CARLESON MEASUREMENTS,) IN RELATION TO GENERALISED FOCK SPACES ASSOCIATED WITH ORTHOGONAL SYSTEMS, AND WITH Q_ SPACES. IN ADDITION, WE INTEND TO STUDY THE CHARACTERISATIONS USING BRUSHLETS OF VALUED HARDY AND BMO BANACH SPACES AND, USING MEASUREMENTS OF INCOMPACITY, WHEN CERTAIN SINGULAR INTEGRAL OPERATORS ARE COMPACT. (English) / rank | |||||||||||||||
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| Property / summary: THE PROPOSED RESEARCH PROJECT IS PART OF THE HARMONIC ANALYSIS. THIS FIELD OF STUDY CONNECTS WITH OTHER AREAS OF WORK, AMONG WHICH WE POINT OUT THE EQUATIONS IN PARTIAL DERIVATIVES, THE THEORY OF NUMBERS AND THE THEORY OF SIGNALS, WHERE THERE ARE NUMEROUS APPLICATIONS OF THE RESULTS OBTAINED IN THE CONTEXT OF THE HARMONIOUS ANALYSIS. IN SPAIN THIS BRANCH OF ANALYSIS OCCUPIES NUMEROUS RESEARCHERS, THERE ARE IN SEVERAL UNIVERSITIES WORKING GROUPS WITH GREAT INTERNATIONAL PRESTIGE. SIGNIFICANT RESULTS HAVE RECENTLY BEEN OBTAINED ON THE NARROWING OF OSCILLATION AND VARIANCE OPERATORS ASSOCIATED WITH OPERATORs’ FAMILIES (E.G. PARTIAL SUMS FOR FOURIER AND WALSH SERIES). WE INTEND TO ANALYSE OSCILLATION AND VARIATION OPERATORS IN DIFFERENT CONTEXTS: CONVERGENCE TO THE DATA IN THE SCHRODINGER EQUATION, ORTHOGONAL AND TRANSFORMED SERIES OF RIESZ FOR THE HEISENBERG GROUP. WE ALSO AIM TO STUDY CERTAIN CLASSES OF ANISOTROPIC SPACES, WHOSE ANISOTROPY IS DESCRIBED BY CONSTANT OR VARIABLE EXPANSIVE MATRICES. IN PARTICULAR, WE INTEND TO STUDY HARDY ANISOTROPIC SPACES WITH VARIABLE EXPONENT. THE HARMONIC ANALYSIS ASSOCIATED WITH ORTHOGONAL SYSTEMS AND SEMI-GROUPS OF OPERATORS HAS BEEN AN ACTIVE AREA OF WORK IN THE LAST DECADE. IN RELATION TO THIS TOPIC WE PROPOSE TO ADDRESS DIFFERENT ISSUES (INDEPENDENT ESTIMATES OF DIMENSION, WEIGHTS, HARDY SPACES,) IN THE CONTEXTS OF LAGUERRE AND BESSEL. IN ADDITION, WE WILL STUDY BANACH MULTIVARIATE LITTLEWOOD-PALEY FUNCTIONS VALUED USING -RADONIFYING OPERATORS, IN ORDER TO OBTAIN CONDITIONS THAT GUARANTEE THE BOUNDING (IN DIFFERENT SPACES) OF MULTIVARIATE MULTIVARIATE MULTIPLIERS DEFINED FOR HERMITE AND LAGUERRE SERIES. THESE RESULTS ON MULTIPLIERS WILL ALLOW US TO CHARACTERISE SOBOLEV BANACH-VALUED SPACES IN THESE CONTEXTS. ON THE OTHER HAND, WE ALSO AIM TO STUDY DIFFERENT ISSUES (ACCOMMODATION AND COMPACTNESS OF OPERATORS, CARLESON MEASUREMENTS,) IN RELATION TO GENERALISED FOCK SPACES ASSOCIATED WITH ORTHOGONAL SYSTEMS, AND WITH Q_ SPACES. IN ADDITION, WE INTEND TO STUDY THE CHARACTERISATIONS USING BRUSHLETS OF VALUED HARDY AND BMO BANACH SPACES AND, USING MEASUREMENTS OF INCOMPACITY, WHEN CERTAIN SINGULAR INTEGRAL OPERATORS ARE COMPACT. (English) / qualifier | |||||||||||||||
point in time: 12 October 2021
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Revision as of 15:18, 12 October 2021
Project Q3147615 in Spain
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | TOPICS IN FOURIER ANALYSIS AND APPLICATIONS |
Project Q3147615 in Spain |
Statements
55,539.0 Euro
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65,340.0 Euro
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85.0 percent
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1 January 2014
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31 December 2017
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UNIVERSIDAD DE LA LAGUNA
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28°29'8.77"N, 16°18'57.38"W
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38023
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EL PROYECTO DE INVESTIGACION PROPUESTO SE ENCUADRA DENTRO DEL ANALISIS ARMONICO. ESTE CAMPO DE ESTUDIO SE CONECTA CON OTRAS AREAS DE TRABAJO, ENTRE LAS QUE SEÑALAMOS LAS ECUACIONES EN DERIVADAS PARCIALES, LA TEORIA DE NUMEROS Y LA TEORIA DE SEÑALES, DONDE SE PRESENTAN NUMEROSAS APLICACIONES DE LOS RESULTADOS OBTENIDOS EN EL CONTEXTO DEL ANALISIS ARMONICO. EN ESPAÑA ESTA RAMA DEL ANALISIS OCUPA A NUMEROSOS INVESTIGADORES, EXISTIENDO EN VARIAS UNIVERSIDADES GRUPOS DE TRABAJO CON GRAN PRESTIGIO INTERNACIONAL. SE HAN OBTENIDO RECIENTEMENTE IMPORTANTES RESULTADOS SOBRE LA ACOTACION DE LOS OPERADORES DE OSCILACION Y DE VARIACION ASOCIADOS A FAMILIAS DE OPERADORES (POR EJEMPLO, LAS SUMAS PARCIALES PARA SERIES DE FOURIER Y WALSH). NOS PROPONEMOS ANALIZAR OPERADORES DE OSCILACION Y DE VARIACION EN DISTINTOS CONTEXTOS: CONVERGENCIA AL DATO EN LA ECUACION DE SCHRODINGER, SERIES ORTOGONALES Y TRANSFORMADAS DE RIESZ PARA EL GRUPO DE HEISENBERG. TENEMOS COMO OBJETIVO TAMBIEN EL ESTUDIO DE CIERTAS CLASES DE ESPACIOS ANISOTROPICOS, CUYA ANISOTROPIA VIENE DESCRITA POR MATRICES EXPANSIVAS CONSTANTES O VARIABLES. EN PARTICULAR, PRETENDEMOS ESTUDIAR ESPACIOS DE HARDY ANISOTROPICOS CON EXPONENTE VARIABLE. EL ANALISIS ARMONICO ASOCIADO A SISTEMAS ORTOGONALES Y A SEMIGRUPOS DE OPERADORES HA SIDO UNA ACTIVA AREA DE TRABAJO EN LA ULTIMA DECADA. EN RELACION CON ESTE TOPICO NOS PROPONEMOS ABORDAR DIFERENTES CUESTIONES (ESTIMACIONES INDEPENDIENTES DE DIMENSION, PESOS, ESPACIOS DE HARDY,¿) EN LOS CONTEXTOS DE LAGUERRE Y BESSEL. ADEMAS, ESTUDIAREMOS FUNCIONES DE LITTLEWOOD-PALEY MULTIVARIANTES BANACH-VALUADAS USANDO OPERADORES -RADONIFYING, AL OBJETO DE OBTENER CONDICIONES QUE GARANTICEN LA ACOTACION (EN DIFERENTES ESPACIOS) DE MULTIPLICADORES MULTIVARIANTES DEFINIDOS PARA SERIES DE HERMITE Y LAGUERRE. ESTOS RESULTADOS SOBRE MULTIPLICADORES NOS PERMITIRAN CARACTERIZAR ESPACIOS DE SOBOLEV BANACH-VALUADOS EN ESTOS CONTEXTOS. POR OTRA PARTE, TENEMOS TAMBIEN COMO OBJETIVO EL ESTUDIO DE DIFERENTES CUESTIONES (ACOTACION Y COMPACIDAD DE OPERADORES, MEDIDAS DE CARLESON,¿) EN RELACION CON ESPACIOS DE FOCK GENERALIZADOS Y ASOCIADOS A SISTEMAS ORTOGONALES, Y CON LOS ESPACIOS Q_. ADEMAS, NOS PROPONEMOS ESTUDIAR LAS CARACTERIZACIONES MEDIANTE BRUSHLETS DE ESPACIOS DE HARDY Y BMO BANACH VALUADOS Y, USANDO MEDIDAS DE NO COMPACIDAD, CUANDO CIERTOS OPERADORES INTEGRALES SINGULARES SON COMPACTOS. (Spanish)
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THE PROPOSED RESEARCH PROJECT IS PART OF THE HARMONIC ANALYSIS. THIS FIELD OF STUDY CONNECTS WITH OTHER AREAS OF WORK, AMONG WHICH WE POINT OUT THE EQUATIONS IN PARTIAL DERIVATIVES, THE THEORY OF NUMBERS AND THE THEORY OF SIGNALS, WHERE THERE ARE NUMEROUS APPLICATIONS OF THE RESULTS OBTAINED IN THE CONTEXT OF THE HARMONIOUS ANALYSIS. IN SPAIN THIS BRANCH OF ANALYSIS OCCUPIES NUMEROUS RESEARCHERS, THERE ARE IN SEVERAL UNIVERSITIES WORKING GROUPS WITH GREAT INTERNATIONAL PRESTIGE. SIGNIFICANT RESULTS HAVE RECENTLY BEEN OBTAINED ON THE NARROWING OF OSCILLATION AND VARIANCE OPERATORS ASSOCIATED WITH OPERATORs’ FAMILIES (E.G. PARTIAL SUMS FOR FOURIER AND WALSH SERIES). WE INTEND TO ANALYSE OSCILLATION AND VARIATION OPERATORS IN DIFFERENT CONTEXTS: CONVERGENCE TO THE DATA IN THE SCHRODINGER EQUATION, ORTHOGONAL AND TRANSFORMED SERIES OF RIESZ FOR THE HEISENBERG GROUP. WE ALSO AIM TO STUDY CERTAIN CLASSES OF ANISOTROPIC SPACES, WHOSE ANISOTROPY IS DESCRIBED BY CONSTANT OR VARIABLE EXPANSIVE MATRICES. IN PARTICULAR, WE INTEND TO STUDY HARDY ANISOTROPIC SPACES WITH VARIABLE EXPONENT. THE HARMONIC ANALYSIS ASSOCIATED WITH ORTHOGONAL SYSTEMS AND SEMI-GROUPS OF OPERATORS HAS BEEN AN ACTIVE AREA OF WORK IN THE LAST DECADE. IN RELATION TO THIS TOPIC WE PROPOSE TO ADDRESS DIFFERENT ISSUES (INDEPENDENT ESTIMATES OF DIMENSION, WEIGHTS, HARDY SPACES,) IN THE CONTEXTS OF LAGUERRE AND BESSEL. IN ADDITION, WE WILL STUDY BANACH MULTIVARIATE LITTLEWOOD-PALEY FUNCTIONS VALUED USING -RADONIFYING OPERATORS, IN ORDER TO OBTAIN CONDITIONS THAT GUARANTEE THE BOUNDING (IN DIFFERENT SPACES) OF MULTIVARIATE MULTIVARIATE MULTIPLIERS DEFINED FOR HERMITE AND LAGUERRE SERIES. THESE RESULTS ON MULTIPLIERS WILL ALLOW US TO CHARACTERISE SOBOLEV BANACH-VALUED SPACES IN THESE CONTEXTS. ON THE OTHER HAND, WE ALSO AIM TO STUDY DIFFERENT ISSUES (ACCOMMODATION AND COMPACTNESS OF OPERATORS, CARLESON MEASUREMENTS,) IN RELATION TO GENERALISED FOCK SPACES ASSOCIATED WITH ORTHOGONAL SYSTEMS, AND WITH Q_ SPACES. IN ADDITION, WE INTEND TO STUDY THE CHARACTERISATIONS USING BRUSHLETS OF VALUED HARDY AND BMO BANACH SPACES AND, USING MEASUREMENTS OF INCOMPACITY, WHEN CERTAIN SINGULAR INTEGRAL OPERATORS ARE COMPACT. (English)
12 October 2021
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San Cristóbal de La Laguna
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Identifiers
MTM2013-44357-P
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