English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We introduce pseudodifferential operators (of infinite order) in the framework of non-quasianalytic classes of Beurling type. We prove that such an operator with (distributional) kernel in a given Beurling class D′ (ω) is pseudo-local and can be locally decomposed, modulo a smoothing operator, as the composition of a pseudodifferential operator of finite order and an ultradifferential operator with constant coefficients in the sense of Komatsu, both operators with kernel in the same class D′ (ω). We also develop the corresponding symbolic calculus. 0. Introduction. The theory of pseudodifferential operators grew out of the study of singular integral operators, and developed after 1965 with the systematic studies of Kohn–Nirenberg [18], Hörmander [14] and others. The study of several problems in classes of (non-quasianalytic) ultradifferentiable functions has also received much attention recently. These are intermediate classes between real analytic functions and C∞ functions. There are essentially two ways to introduce them: the theory of Komatsu [16], in which one looks at the growth of the derivatives on compact sets, and the theory developed by Björk [2] in 1966, following the ideas previously announced by Beurling, in which one pays attention to the growth of the Fourier transforms. We will work with ultradifferentiable functions as defined by Braun, Meise and Taylor [8]. Their point of view permits a unified treatment of both theories, contains the most relevant cases of Komatsu’s theory and is strictly broader than Beurling–Björk’s. Pseudodifferential operators (of finite or infinite order) on Gevrey classes have been extensively studied by many authors ([5], [6], [15], [20], [25] among others). We refer to [23] for an excellent introduction to this topic. For more general classes of ultradifferentiable functions, following the approach of 2000 Mathematics Subject Classification: 46F05, 47G30, 35S05, 46E10.

Pseudodifferential operators on non-quasianalytic classes of Beurling type