Results 61 to 70 of about 152 (97)

On Ultradifferentiable Regularity of Perturbations by Lower Order Terms of Globally $$C^\infty$$ Hypoelliptic Ultradifferentiable Pseudodifferential Operators

Journal of Fourier Analysis and Applications, 2023
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Igor Ambo Ferra, Gerson Petronilho
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Operator enumeration in ultradifferentiable vectors

Ukrainian Mathematical Journal, 1992
See the review in Zbl 0777.47014.
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Hankel–Clifford transformations on some ultradifferentiable function spaces and pseudo-differential operators

Journal of Pseudo-Differential Operators and Applications, 2013
The authors study a class of pseudodifferential operators, based on using, instead of the Fourier transform, the so-called first Hankel-Clifford transformation \[ \hat{\varphi}(y)=y^\mu \int\limits_0^\infty C_\mu (xy)\varphi (x)\,dx, \] where \(\mu \geq 0\), \(C_\mu (x)=x^{-\mu /2}J_\mu (2x^{1/2})\), \(J_\mu\) is the Bessel function.
Prasad, Akhilesh, Kumar, Sumant
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Pseudodifferential operators involving linear canonical Hankel transformations on some ultradifferentiable function spaces

Mathematical Methods in the Applied Sciences, 2020
In this work, continuity of linear canonical Hankel transformation on the ultradifferentiable function spaces are discussed. Furthermore, the pseudodifferential operator associated with linear canonical Hankel transformation is shown to be the continuous linear mapping from one ultradifferentiable function space to another.
Tanuj Kumar, Akhilesh Prasad
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Spectrum of the Cesàro Operator on the Ultradifferentiable Function Spaces $${\mathcal E}_\omega ({\mathbb {R}}_+)$$

Complex Analysis and Operator Theory, 2021
The paper investigates certain properties of the Cesàro operator \(C\) on the spaces \(\mathscr{E}_{[\omega]}(\mathbb{R}_+)\) of ultradifferentiable functions of Roumieu and Beurling type (in the sense of \textit{R. W. Braun} et al. [Result. Math. 17, No.
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On certain linear operators in spaces of ultradifferentiable functions

Results in Mathematics, 1996
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Global $${\mathcal {M}}-$$Hypoellipticity, Global $${\mathcal {M}}-$$Solvability and Perturbations by Lower Order Ultradifferential Pseudodifferential Operators

Journal of Fourier Analysis and Applications, 2020
The paper concerns the problem of the hypoellipticity for pseudo-differential operators. Namely, the authors define classes of ultra-diffferentiable functions on the \(n\)-torus, including as particular cases Gevrey and analytic classes. The corresponding Gevrey-Sobolev and ultra-distributions are also considered.
Ferra, Igor Ambo, Petronilho, Gerson, de Lessa Victor, Bruno   +2 more
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Ultradifferential operators in the study of Gevrey solvability and regularity

Mathematische Nachrichten, 2018
AbstractIn this work we present a new representation formula for ultradistributions using the so‐called ultradifferential operators. The main difference between our representation result and other works is that here we do not break the duality of Gevrey functions of other s and their ultradistributions, i.e., we locally represent an element of by an ...
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Surjective Partial Differential Operators on Spaces of Ultradifferentiable Functions of Roumieu Type

Results in Mathematics, 1996
As is already classical, linear partial differential operators \(P(D)\) with constant coefficients are not necessarily surjective on the space \({\mathcal A}(\Omega)\) of real analytic functions even if \(\Omega\) is convex. The same difficulty was found for the space of Roumieu type ultradifferentiable functions, which was caused by the similarity of ...
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On the continuous linear right inverse for convolution operators in spaces of ultradifferentiable functions

Mathematical Notes, 2014
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