Fundamental results for pseudo-differetial operators of type 1,1

This paper develops some deeper consequences of an extended definition, proposed previously by the author, of pseudo-differential operators that are of type $1,1$ in H\"ormander's sense. Thus, it contributes to the long-standing problem of creating a systematic theory of such operators. It is shown that type $1,1$-operators are defined and continuous on the full space of temperate distributions, if they fulfil H\"ormander's twisted diagonal condition, or more generally if they belong to the self-adjoint subclass; and that they are always defined on the temperate smooth functions. As a main tool the paradifferential decomposition is derived for type $1,1$-operators, and to confirm a natural hypothesis the symmetric term is shown to cause the domain restrictions; whereas the other terms are shown to define nice type $1,1$-operators fulfilling the twisted diagonal condition. The decomposition is analysed in the type $1,1$-context by combining the Spectral Support Rule and the factorisation inequality, which gives pointwise estimates of pseudo-differential operators in terms of maximal functions.Comment: 40 pages. Contents identical to version published on 16 May 2016 by Axioms (only the styles differ

BISON: we're in this together

Librarians involved in assisting researchers with planning, execution and documentation of systematic literature searches are well aware of the considerable amount of practice required to conduct reliable, transparent, and reproducible literature searches. In addition to building the necessary skills and knowledge, factors such as changes in databases, updates in standards or methodologies, and development of new tools makes it difficult to keep up to date. In response an online community of practice has been established in Norway to serve as a platform for facilitating knowledge sharing in these areas. However, building and maintaining an active community is not an easy task. This article describes the development, the activities, the challenges, and the possible future for the community