Fractal Sobolev systems of functions associated with orthonormal systems of functions

Islam, Md. N. ; Kaish, I. ; Akhtar, Md. N. ; Navascués, M. A. (Universidad de Zaragoza)

Resumen: This paper introduces the α-fractal Sobolev system of functions corresponding to Sobolev orthonormal system of functions. An approximation-related result similar to Weierstrass theorem is derived. It is shown that the set of α-fractal versions of Sobolev sums is dense and complete in the weighted Sobolev space Wr,2ρ(I). A Schauder basis and a Riesz basis of fractal type for the space Wr,2ρ(I) are found. The Fourier–Sobolev expansion of an α-fractal function fα corresponding to a certain set of interpolation points is presented. Moreover, some results on convergence of Fourier–Sobolev expansion of fα with respect to uniform norm and Sobolev norm are established.

Idioma: Inglés

DOI: 10.1142/S1793557122502035

Año: 2022

Publicado en: Asian-European Journal of Mathematics 15, 11 (2022)
ISSN: 1793-5571

Factor impacto CITESCORE: 1.3 - Mathematics (Q3)

Factor impacto SCIMAGO: 0.321 - Mathematics (miscellaneous) (Q3)

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)