The Segal Algebra S0(\Bbb Rd) and Norm Summability of Fourier Series and Fourier Transforms

• Autores: Hans G. Feichtinger, Ferenc Weisz
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 148, Nº 4, 2006, págs. 333-349
• Idioma: inglés
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• Resumen

  • A general summability method, the so-called ?-summability is considered for multi-dimensional Fourier series. Equivalent conditions are derived for the uniform and L 1-norm convergence of the ?-means s n ? f to the function f. If f is in a homogeneous Banach space, then the preceeding convergence holds in the norm of the space. In case ? is an element of Feichtinger¿s Segal algebra , then these convergence results hold. Some new sufficient conditions are given for ? to be in . A long list of concrete special cases of the ?-summation is listed. The same results are also provided in the context of Fourier transforms, indicating how proofs have to be changed in this case