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Small functions and iterative methods

Michal Fečkan (1992)

Commentationes Mathematicae Universitatis Carolinae

Iterative methods based on small functions are used both to show local surjectivity of certain operators and a fixed point property of mappings on scales of complete metric spaces.

Solution operators for convolution equations on the germs of analytic functions on compact convex sets in ℂ N

S. Melikhov, Siegfried Momm (1995)

Studia Mathematica

G ⊂ ℂ N is compact and convex it is known for a long time that the nonzero constant coefficients linear partial differential operators (of finite or infinite order) are surjective on the space of all analytic functions on G. We consider the question whether solutions of the inhomogeneous equation can be given in terms of a continuous linear operator. For instance we characterize those sets G for which this is always the case.

Solvability of the functional equation f = (T-I)h for vector-valued functions

Ryotaro Sato (2004)

Colloquium Mathematicae

Let X be a reflexive Banach space and (Ω,,μ) be a probability measure space. Let T: M(μ;X) → M(μ;X) be a linear operator, where M(μ;X) is the space of all X-valued strongly measurable functions on (Ω,,μ). We assume that T is continuous in the sense that if (fₙ) is a sequence in M(μ;X) and l i m n → ∞ f ₙ = f in measure for some f ∈ M(μ;X), then also l i m n → ∞ T f ₙ = T f in measure. Then we consider the functional equation f = (T-I)h, where f ∈ M(μ;X) is given. We obtain several conditions for the existence of h ∈ M(μ;X) satisfying...

Some theorems on the stability of numerical processes

Solomon G. Mikhlin (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Nell’articolo si dimostrano alcuni teoremi sulla stabilità dei processi numerici di Ritz e della collocazione in rapporto agli errori di «distorsione».

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