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Some remarks on convolution equations

C. A. Berenstein, M. A. Dostal (1973)

Annales de l'institut Fourier

Using a description of the topology of the spaces E ' ( Ω ) ( Ω open convex subset of R n ) via the Fourier transform, namely their analytically uniform structures, we arrive at a formula describing the convex hull of the singular support of a distribution T , T ∈ E ' . We give applications to a class of distributions T satisfying cv. sing. supp. S * T = cv. sing. supp. S + cv. sing. supp. T for all S ∈ E ' .

Some remarks on descriptive characterizations of the strong McShane integral

Sokol Bush Kaliaj (2019)

Mathematica Bohemica

We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function f : W → X defined on a non-degenerate closed subinterval W of ℝ m in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure V ℳ F generated by the primitive F : ℐ W → X of f , where ℐ W is the family of all closed non-degenerate subintervals of W .

Some remarks on generalised lush spaces

Jan-David Hardtke (2015)

Studia Mathematica

D. Tan, X. Huang and R. Liu [Studia Math. 219 (2013)] recently introduced the notion of generalised lush (GL) spaces, which, at least for separable spaces, is a generalisation of the concept of lushness introduced by Boyko et al. [Math. Proc. Cambridge Philos. Soc. 142 (2007)]. The main result of D. Tan et al. is that every GL-space has the so called Mazur-Ulam property (MUP). In this note, we prove some further properties of GL-spaces, for example, every M-ideal in a...

Some remarks on Gleason measures

P. De Nápoli, M. C. Mariani (2007)

Studia Mathematica

This work is devoted to generalizing the Lebesgue decomposition and the Radon-Nikodym theorem to Gleason measures. For that purpose we introduce a notion of integral for operators with respect to a Gleason measure. Finally, we give an example showing that the Gleason theorem does not hold in non-separable Hilbert spaces.

Currently displaying 561 – 580 of 1282