Convergence des martingales pluri-sous-harmoniques vectorielles à deux indices
Convergence diffuse d'une suite de fonctions
Convergence in spaces of rapidly increasing distributions.
Convergence in the dual of certain -spaces
Convergence in the generalized sense relative to Banach algebras of operators and in LMC-algebras
The notion of convergence in the generalized sense of a sequence of closed operators is generalized to the situation where the closed operators involved are affiliated with a Banach algebra of operators. Also, the concept of convergence in the generalized sense is extended to the context of a LMC-algebra, where it applies to the spectral theory of the algebra.
Convergence of convex functions and generalized inf-convolutive approximations. (Convergences des fonctions convexes et approximations inf-convolutives généralisées.)
Convergence of convolution operators
Convergence of derivations on nearest algebras.
Convergence of generalized eigenfunction expansions.
Convergence of greedy approximation I. General systems
We consider convergence of thresholding type approximations with regard to general complete minimal systems eₙ in a quasi-Banach space X. Thresholding approximations are defined as follows. Let eₙ* ⊂ X* be the conjugate (dual) system to eₙ; then define for ε > 0 and x ∈ X the thresholding approximations as , where . We study a generalized version of that we call the weak thresholding approximation. We modify the in the following way. For ε > 0, t ∈ (0,1) we set and consider the weak...
Convergence of greedy approximation II. The trigonometric system
We study the following nonlinear method of approximation by trigonometric polynomials. For a periodic function f we take as an approximant a trigonometric polynomial of the form , where is a set of cardinality m containing the indices of the m largest (in absolute value) Fourier coefficients f̂(k) of the function f. Note that Gₘ(f) gives the best m-term approximant in the L₂-norm, and therefore, for each f ∈ L₂, ||f-Gₘ(f)||₂ → 0 as m → ∞. It is known from previous results that in the case of...
Convergence of orthogonal series of projections in Banach spaces
For a sequence of mutually orthogonal projections in a Banach space, we discuss all possible limits of the sums in a “strong” sense. Those limits turn out to be some special idempotent operators (unbounded, in general). In the case of X = L₂(Ω,μ), an arbitrary unbounded closed and densely defined operator A in X may be the μ-almost sure limit of (i.e. μ-a.e. for all f ∈ (A)).
Convergence of Rothe's method in Hölder spaces
The convergence of Rothe’s method in Hölder spaces is discussed. The obtained results are based on uniform boundedness of Rothe’s approximate solutions in Hölder spaces recently achieved by the first author. The convergence and its rate are derived inside a parabolic cylinder assuming an additional compatibility conditions.
Convergence of series and isomorphic embeddings in Banach spaces
Convergence of Taylor series in Hardy and Besov spaces.
Convergence of the dual greedy algorithm in Banach spaces.
Convergence of Tight Asymptotic Martingales in a Banach Space.
Convergence of vectorial continued fractions related to the spectral seminorm.
Convergence structures and -asymptotic behaviour of Fourier hyperfunctions.
Convergence theorems for Banach space valued integrable multifunctions.