Fractal frames of functions on the rectangle

Navascués Sanagustín, María Antonia (Universidad de Zaragoza) ; Mohapatra, Ram ; Akhtar, Md Nasim

Resumen: In this paper, we define fractal bases and fractal frames of L2(I   J), where I and J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification of L2(I   J) with the tensor product space L2(I) NL2(J). First, we recall the procedure of constructing a fractal perturbation of a continuous or integrable function. Then, we define fractal frames and bases of L2(I   J) composed of product of such fractal functions. We also obtain weaker families as Bessel, Riesz and Schauder sequences for the same space. Additionally, we study some properties of the tensor product of the fractal operators associated with the maps corresponding to each variable.

Idioma: Inglés

DOI: 10.3390/fractalfract5020042

Año: 2021

Publicado en: Fractal and fractional 5, 42 (2021), [15 pp.]
ISSN: 2504-3110

Factor impacto JCR: 3.577 (2021)

Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 18 / 108 = 0.167 (2021) - Q1 - T1

Factor impacto CITESCORE: 2.8 - Mathematics (Q2) - Physics and Astronomy (Q3)

Factor impacto SCIMAGO: 0.644 - Statistical and Nonlinear Physics (Q2) - Analysis (Q2)

Tipo y forma: Article (Published version)

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