Intersection properties of weak analytically uniform classes of functions

Liess, Otto

doi:10.1007/bf02385827

Cited by 14 publications

(8 citation statements)

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“…As a generalization of the Gevrey classes, we may consider the inhomogeneous Gevrey classes associated to a weight function λ according to Liess [17] and Liess-Rodino [18]. Their definition, in terms of Fourier transform, is recalled at the beginning of Section 2.…”

Section: Definition 11mentioning

confidence: 99%

Inhomogeneous Gevrey classes and ultradistributions

Calvo

Morando

Rodino

2004

Journal of Mathematical Analysis and Applications

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The inhomogeneous Gevrey classes, defined in terms of Fourier transform, are a natural extension of the standard Gevrey classes. We find equivalent characterizations and discuss algebraic and topological properties. We therefore introduce the dual spaces, the inhomogeneous ultradistributions, giving some equivalent definitions and corresponding algebraic and topological properties; in particular, a version of the Paley–Wiener–Schwartz theorem is proved in our framework. Finally, as an important example, the multianisotropic Gevrey classes and ultradistributions are considered

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Section: Definition 11mentioning

confidence: 99%

Inhomogeneous Gevrey classes and ultradistributions

Calvo

Morando

Rodino

2004

Journal of Mathematical Analysis and Applications

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“…The paper is devoted to a generalization of the standard Gevrey classes, that includes two important extensions present in the literature: the inhomogeneous Gevrey classes introduced by Liess 15 (cf. also Liess‐Rodino 16 and Calvo et al 9) and the ultradifferentiable functions, treated by many authors, among which Roumieu 21, Komatsu 13 and Braun‐Meise‐Taylor 4.…”

Section: Introductionmentioning

confidence: 99%

“…The second generalization of the standard Gevrey classes is via formula (1.2), and is represented by the inhomogeneous Gevrey classes introduced by Liess 15 (cf. also 9 and 16).…”

Section: Introductionmentioning

confidence: 99%

“… Abstract We present a generalization of Gevrey classes, aiming at including the inhomogeneous Gevrey functions introduced by Liess 15 and the ultradifferentiable functions in the sense of Braun et al 4. Therefore, we treat the related dual spaces, called generalized Gevrey ultradistributions, proving also a version of the Paley‐Wiener‐Schwartz Theorem in our framework.…”

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confidence: 99%

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On some generalizations of Gevrey classes

Calvo

Gómez-Collado

2011

Math. Nachr.

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We present a generalization of Gevrey classes, aiming at including the inhomogeneous Gevrey functions introduced by Liess [15] and the ultradifferentiable functions in the sense of Braun et al. [4]. Therefore, we treat the related dual spaces, called generalized Gevrey ultradistributions, proving also a version of the Paley-Wiener-Schwartz Theorem in our framework. Two different topologies are treated, following the lines both of Beurling [1] and of Roumieu [21], [22]. We finally treat in these spaces the well-posedness of the Cauchy problem for weakly hyperbolic operators, extending the previous results of Larsson [14] and Calvo [6], [7].

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“…We denote by G (X) the set of all feCD' (X) which are of class Liess [6] and the references there. The advantage of the prŝ ent definition is that it can be microlocalized in a natural way, adapting the procedure used by Rodino [10] in the C°°f ramework.…”

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confidence: 99%