EFFECTIVE REGULARITY CRITERIA FOR ANALYTIC MAPPINGS

Gevrey Regularity of Invariant Curves of Analytic Reversible Mappings

We prove the existence of a Gevrey family of invariant curves for analytic reversible mappings under weaker nondegeneracy condition. The index of the Gevrey smoothness of the family could be any number μ > τ 2, where τ > m − 1 is the exponent in the small divisors condition and m is the order of degeneracy of the reversible mappings. Moreover, we obtain a Gevrey normal form of the reversible ma...

Complex Analytic Mappings

The Convenient Setting for Real Analytic Mappings

We present here ”the” cartesian closed theory for real analytic mappings. It is based on the concept of real analytic curves in locally convex vector spaces. A mapping is real analytic, if it maps smooth curves to smooth curves and real analytic curves to real analytic curves. Under mild completeness conditions the second requirement can be replaced by: real analytic along affine lines. Enclose...

Weighted analytic regularity in polyhedra

We explain a simple strategy to establish analytic regularity for solutions of second order linear elliptic boundary value problems. The abstract framework presented here helps to understand the proof of analytic regularity in polyhedral domains given in the authors’ paper in Math. Models Methods Appl. Sci. 22 (8) (2012). We illustrate this strategy by considering problems set in smooth domains...

Criteria of regularity for norm-sequences. II

Abstract. The regularity property of a norm-sequence ρ(n) = ‖Tn‖ (n ∈ N) ensures that the operator T can be intertwined with an isometry V , which relation can be exploited to obtain a lot of information for T itself, as it was shown in [1] and [2]. In [3] general sufficient conditions of regularity were provided. In the present note a necessary and sufficient condition of regularity is given. ...