Results 31 to 40 of about 105 (96)

On the Carleman classes of vectors of a scalar type spectral operator

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 60, Page 3219-3235, 2004., 2004
The Carleman classes of a scalar type spectral operator in a reflexive Banach space are characterized in terms of the operator′s resolution of the identity. A theorem of the Paley‐Wiener type is considered as an application.
Marat V. Markin
wiley   +1 more source

A note on the spectral operators of scalar type and semigroups of bounded linear operators

International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 10, Page 635-640, 2002., 2002
It is shown that, for the spectral operators of scalar type, the well‐known characterizations of the generation of C0‐ and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup ...
Marat V. Markin
wiley   +1 more source

Extension of ultradifferentiable functions

Manuscripta Mathematica, 1994
The extension problem considered in this paper is of the type given below: Let \(K_1\) and \(K\) be compact convex sets such that \(\text{int} (K_1) \supset K\), and such that \(\text{int} (K)\neq \emptyset\) or \(K= \{0\}\) and let a sequence \((N_a)\) of positive numbers be given.
openaire   +1 more source

Construction of the log‐convex minorant of a sequence {Mα}α∈N0d$\lbrace M_\alpha \rbrace _{\alpha \in \mathbb {N}_0^d}$

Mathematische Nachrichten, Volume 298, Issue 2, Page 456-477, February 2025.
Abstract We give a simple construction of the log‐convex minorant of a sequence {Mα}α∈N0d$\lbrace M_\alpha \rbrace _{\alpha \in \mathbb {N}_0^d}$ and consequently extend to the d$d$‐dimensional case the well‐known formula that relates a log‐convex sequence {Mp}p∈N0$\lbrace M_p\rbrace _{p\in \mathbb {N}_0}$ to its associated function ωM$\omega _M$, that
Chiara Boiti, David Jornet, Alessandro Oliaro, Gerhard Schindl   +3 more
wiley   +1 more source

The Metivier inequality and ultradifferentiable hypoellipticity

Mathematische Nachrichten, Volume 297, Issue 7, Page 2517-2531, July 2024.
Abstract In 1980, Métivier characterized the analytic (and Gevrey) hypoellipticity of L2$L^2$‐solvable partial linear differential operators by a priori estimates. In this note, we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy–Carleman classes given by suitable weight sequences. We also discuss the case when
Paulo D. Cordaro, Stefan Fürdös
wiley   +1 more source

An Introduction to Extended Gevrey Regularity

Axioms
Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example, when ...
Nenad Teofanov, Filip Tomić, Milica Žigić   +2 more
doaj   +1 more source

Division by Flat Ultradifferentiable Functions and Sectorial Extensions [PDF]

Results in Mathematics, 2003
We consider classes $ \mathcal{A}_M(S) $ of functions holomorphic in an open plane sector $ S $ and belonging to a strongly non-quasianalytic class on the closure of $ S $. In $ \mathcal{A}_M(S) $, we construct functions which are flat at the vertex of $ S $ with a sharp rate of vanishing.
openaire   +4 more sources

Eigenfunction expansions of ultradifferentiable functions and ultradistributions. II. Tensor representations [PDF]

Transactions of the American Mathematical Society, Series B, 2018
In this paper we analyse the structure of the spaces of coefficients of eigenfunction expansions of functions in Komatsu classes on compact manifolds, continuing the research in our paper [Trans. Amer. Math. Soc. 368 (2016), pp.8481-8498]. We prove that such spaces of Fourier coefficients are perfect sequence spaces.
Dasgupta, A, Ruzhansky, M
openaire   +6 more sources

Holomorphic approximation of ultradifferentiable functions

Mathematische Annalen, 1981
Introduct ion Let S be a closed subset of some open set in Cn and denote by dT(S) the space of germs of holomorphic functions on (a neighborhood of) S. For a space F(S) of tEvalued (continuous, differentiable etc.) functions on S [containing t~(S)] the problem of holomorphic approximation consists of finding conditions to ensure that the natural ...
openaire   +1 more source

Convolution equations for ultradifferentiable functions and ultradistributions

Journal of Mathematical Analysis and Applications, 2004
For convolution operators acting on spaces of ultradistributions of Beurling type on open sets, the authors characterize the surjectivity of the operator (modulo ultrasmooth functions) in terms of a convexity condition for singular supports in the spirit of Hörmander's convexity conditions (Theorem A).
Frerick, L., Wengenroth, J.
openaire   +1 more source