Analytic and Luzin spaces (non-separable case)

Analytic approximations of norms in separable Banach spaces

Evolution inclusions in non separable Banach spaces

We study a Cauchy problem for non-convex valued evolution inclusions in non separable Banach spaces under Filippov type assumptions. We establish existence and relaxation theorems.

Non - separable Banach spaces with non - meager Hamel basis

We show that an infinite-dimensional complete linear space X has: • a dense hereditarily Baire Hamel basis if |X| ≤ c; • a dense non-meager Hamel basis if |X| = κ = 2 for some cardinal κ. According to Corollary 3.4 of [BDHMP] each infinite-dimensional separable Banach space X has a non-meager Hamel basis. This is a special case of Theorem3.3 of [BDHMP], asserting that an infinite-dimensional Ba...

Chromatic derivatives and non-separable inner product spaces

We present a detailed motivation for the notions of the chromatic derivatives and the chromatic expansions. The chromatic derivatives are special, numerically robust linear differential operators. The chromatic expansions are the associated local expansions, which possess features of both the Taylor and the Nyquist expansions. We give simplified treatment of some of the basic properties of the ...

Descent for Non-archimedean Analytic Spaces

In the theory of schemes, faithfully flat descent is a very powerful tool. One wants a descent theory not only for quasi-coherent sheaves and morphisms of schemes (which is rather elementary), but also for geometric objects and properties of morphisms between them. In rigid-analytic geometry, descent theory for coherent sheaves was worked out by Bosch and Görtz [BG, 3.1] under some quasi-compac...