Título original | Sulle equazioni alle differenze con incrementi variabili. |
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Título inglés | On difference equations with variable increments. |
Título español | Ecuaciones en diferencias con incrementos variables. |
Autor/es | Borelli Forti, Constanza ; Fenyö, István |
Organización | Ist. Mat. F. Enriques Univ. Studi Milano, Milán, Italia |
Revista | 0210-7821 |
Publicación | 1980, 4 (2): 93-101, 2 Ref. |
Tipo de documento | articulo |
Idioma | Italiano |
Resumen inglés | Let X be an arbitrary Abelian group and E a Banach space. We consider the difference-operators ∆n defined by induction: (∆f)(x;y) = f(x+y) - f(x), (∆nf)(x;y1,...,yn) = (∆n-1(∆f)(.;y1)) (x;y2,...,yn) (n = 2,3,4,..., ∆1=∆, x,yi belonging to X, i = 1,2,...,n; f: X --> E). Considering the difference equation (∆nf)(x;y1,y2,...,yn) = d(x;y1,y2,...,yn) with independent variable increments, the most general solution is given explicitly if d: X x Xn --> E is a given bounded function. Also the most general form of bounded functions in the range of ∆n is determined. Another type of operator, designed by ∆2n is defined by (∆2f)(x;y) = f(x+2y) - 2f(x+y) + f(x), (∆2nf)(x;y1,...,yn) = (∆2n-1(∆2f)(.;y1)) (x;y2,...,yn), (n = 2,3,4,..., ∆21=∆2, x,yi belonging to X, i = 1,2,...,n) and under the same conditions as above the most general solution of the equation ∆2nf = d is established. |
Clasificación UNESCO | 120207 |
Palabras clave español | Ecuaciones en diferencias ; Incrementos variables |
Código MathReviews | MR0599135 |
Código Z-Math | Zbl 0456.39002 |
Acceso al artículo completo |