In recent years, Fourier multiplier theorems in vector–valued function spaces have found many applications in embedding theorems of abstract function spaces and in theory of differential operator equations, especially in maximal regularity of parabolic and elliptic differential–operator equations. Operator–valued multiplier theorems in Banach–valued function spaces have been discussed extensive...

The embedding theorems in anisotropic Besov-Lions type spaces Bp,θ(R ;E0,E) are studied; here E0 and E are two Banach spaces. The most regular spaces Eα are found such that the mixed differential operators Dα are bounded from Bp,θ(R ;E0,E) to B q,θ(R ;Eα), where Eα are interpolation spaces between E0 and E depending on α= (α1,α2, . . . ,αn) and l = (l1, l2, . . . , ln). By using these results t...

VECTORIAL SEMANTICS AND SYNTAX OF LINEAR LOGICWith finiteness spaces, Ehrhard has shown a semantics of linear logic with a differentiationoperation. In this framework, the interpretation of formulas can be represented as Taylor series.This has led to the introduction of a differential syntax. This thesis in denotational semanticspursues this work through an exploration of ve...

In this paper the notion of an M -th order invariant bilinear differential pairing is introduced and a formal definition is given. If the manifold has an AHS structure, then various first order pairings are constructed. This yields a classification of all first order invariant bilinear differential pairings on homogeneous spaces with an AHS structure except for certain totally degenerate cases....

This study focuses on anisotropic Sobolev type spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E, depending of α and order of spaces are found that ...

This paper reports "work in progress" on a project which I've titled, "The Spaces of Transnational Cultures". The aim of the project is to build on, but be methodologically different from, my earlier research on the architecture and urbanism of colonial and postcolonial cities in which the principal objective had been to demonstrate the inherently constitutive relationship between the political...

For transcendental values of q the quantum tangent spaces of all left-covariant first order differential calculi of dimension less than four on the quantum group SLq(2) are given. All such differential calculi Γ are determined and investigated for which the left-invariant differential one-forms ω(u2), ω(u 2 1) and ω(u 1 1 − u 2 2) generate Γ as a bimodule and the universal higher order differen...

Many natural spaces of functions form infinite-dimensional vector spaces. Examples are the space of polynomials and the space of smooth functions. If we are interested in solving differential equations, then, it is important to understand analysis in infinite-dimensional vector spaces (over R or C). First of all, we should recognize the following straightforward fact about finite-dimensional ve...