Translaciono invarijantni Banahovi prostori distribucija i granične vrednosti preko integralne transformacije [PDF]
, 2015 We use common notation ∗ for distribution (Scshwartz), (Mp) (Beurling) i {Mp} (Roumieu) setting. We introduce and study new (ultra) distribution spaces, the test function spaces D∗E and their strong duals D'∗E’*.These spaces generalize the spaces D∗Lq ,
Димовски, Павел
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On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the open semi-axis [PDF]
Open Mathematics, 2019 Abstract Given the abstract evolution equation $$\begin{array}{} \displaystyle y'(t)=Ay(t),\, t\ge 0, \end{array}$$ with scalar type spectral operator A in a complex Banach space, found are conditions necessary and sufficient for all weak solutions of the equation, which a priori need not be strongly differentiable, to be strongly Gevrey ...
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Extension of Localisation Operators to Ultradistributional Symbols With Super-Exponential Growth
In the Gelfand-Shilov setting, the localisation operator $A^{\varphi_1,\varphi_2}_a$ is equal to the Weyl operator whose symbol is the convolution of $a$ with the Wigner transform of the windows $\varphi_2$ and $\varphi_1$. We employ this fact, to extend
Pilipović, Stevan +2 more
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On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator of orders less than one [PDF]
Open Mathematics, 2019 Abstract It is shown that, if all weak solutions of the evolution equation $$\begin{array}{} \displaystyle y'(t)=Ay(t),\, t\ge 0, \end{array} $$ with a scalar type spectral operator A in a complex Banach space are Gevrey ultradifferentiable of orders less than one, then the operator A is necessarily bounded.
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On Kernels of Convolution Operators in the Roumieu Spaces of Ultradifferentiable Functions
Владикавказский математический журналВ работе исследуются операторы свертки в пространствах Румье ультрадифференцируемых функций нормального типа на числовой прямой. К данному классу пространств относятся известные классы Жевре. В качестве частных случаев операторы свертки включают в себя дифференциальные операторы бесконечного порядка с постоянными коэффициентами, дифференциально ...
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Hypoellipticity of analytic differential operators in general ultradifferentiable classes
We show that analytic pseudodifferential and Fourier integral operators behave well for ultradifferentiable classes satisfying minimal regularity properties. As an application we investigate the ultradifferentiable regularity properties of several examples of analytic differential operators.
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On the Carleman ultradifferentiable vectors of a scalar type spectral operator
, 2016 Published in Methods of Functional Analysis and Topology (MFAT), available at http://mfat.imath.kiev.ua/article/?id=838.
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Kyoto Journal of Mathematics, 2000 The author gives a direct proof of the perfect block diagonalization of systems of pseudo-differential operators in the ultradifferentiable classes. The same result was already proved by a successive approximation, but not directly.
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The Baouendi-Treves approximation Theorem for Gevrey classes and applications
, 2019 In this work we show how to extend the seminal Baouendi-Treves approximation theorem for Gevrey functions and ultradistributions. As applications we present a Gevrey version of the approximate Poincar\'e Lemma and study ultradistributions vanishing on ...
Hoepfner, Gustavo +2 more
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Decomposition theorems for the temperature functions with singularity [PDF]
, 1999 Chung, Soon-Yeong
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