A simple proof of Kotake–Narasimhan theorem in some classes of ultradifferentiable functions

@article{Boiti2016ASP,
  title={A simple proof of Kotake–Narasimhan theorem in some classes of ultradifferentiable functions},
  author={Chiara Boiti and David Jornet},
  journal={Journal of Pseudo-Differential Operators and Applications},
  year={2016},
  volume={8},
  pages={297-317}
}
  • C. Boiti, D. Jornet
  • Published 13 April 2016
  • Mathematics
  • Journal of Pseudo-Differential Operators and Applications
We give a simple proof of a general theorem of Kotake–Narasimhan for elliptic operators in the setting of ultradifferentiable functions in the sense of Braun, Meise and Taylor. We follow the ideas of Komatsu. Based on an example of Métivier, we also show that the ellipticity is a necessary condition for the theorem to be true. 
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References

SHOWING 1-10 OF 42 REFERENCES
The Problem of Iterates in Some Classes of Ultradifferentiable Functions
We consider the problem of iterates in some spaces of ultradifferentiable classes in the sense of Braun, Meise and Taylor. In particular, we obtain a microlocal version, in this setting of functions,
A Paley-Wiener type theorem for generalized non-quasianalytic classes
Let P be a hypoelliptic polynomial. We consider classes of ultradifferentiable functions with respect to the iterates of the partial differential operator P (D) and prove that such classes satisfy a
A proof of Kotake and Narasimhan's theorem.
We shall give a simple proof of the following theorem announced by Kotak and Narasimhan [1. Theorem. Let P=P(x, D) be a linear elliptic differential operator of order m with analytic coecients in a
Superposition in Classes of Ultradifferentiable Functions
We present a complete characterization of the classes of ultradifferentiable functions that are holomorphically closed. Moreover, we show that any class holomorphically closed is also closed under
Ultradifferentiable functions and Fourier analysis
Classes of non-quasianalytic functions are classically defined by imposing growth conditions on the derivatives of the functions. It was Beuding [1] (see Bjorck [2]) who pointed out that decay
A comparison of two different ways to define classes of ultradifferentiable functions
We characterize the weight sequences (Mp)p such that the class of ultradifferentiable functions E(Mp) defined by imposing conditions on the derivatives of the function in terms of this sequence
On the functional dimension of solution spaces of hypoelliptic partial differential operators
Soit N p l'espace des solutions C ∞ de l'equation P(D)f=0 definie sur R N . On demontre que dfN p =lim t→∞ m(logv(t)/logt)+1, m=degP(P operateurs hypoelliptiques), ou v(t):=λ{x∈R n−1 |P(x,0)|≤t},
Iterates and Hypoellipticity of Partial Differential Operators on Non-Quasianalytic Classes
Let P be a linear partial differential operator with constant coefficients. For a weight function ω and an open subset Ω of $${\mathbb{R}^N}$$ , the class $${\mathcal{E}_{P,\{\omega\}}(\Omega)}$$ of
The growth of hypoelliptic polynomials and Gevrey classes
For given hypoelliptic polynomials P and Q, classes r^(O) and rg(fl) involving Gevrey type estimates on the successive iterates of the corresponding differential operators are defined. The
Wave Front Sets with respect to the Iterates of an Operator with Constant Coefficients
We introduce the wave front set with respect to the iterates of a hypoelliptic linear partial differential operator with constant coefficients of a classical distribution in an open set Ω in the
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