Results 101 to 110 of about 3,122,419 (133)

On Generalized Definitions of Ultradifferentiable Classes [PDF]

Journal of Mathematical Analysis and Applications, 2023
We show that the ultradifferentiable-like classes of smooth functions introduced and studied by S. Pilipovi\'c, N. Teofanov and F. Tomi\'c are special cases of the general framework of spaces of ultradifferentiable functions defined in terms of weight ...
Gerhard Schindl, Javier Jiménez Garrido, David Nicolas Nenning   +2 more
exaly   +2 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 ...
Bernd Droste
exaly   +2 more sources

Ultradifferentiable Functions on Lines in ℝⁿ [PDF]

Proceedings of the American Mathematical Society, 1999
It is well known that a function f ∈
exaly   +2 more sources

Extension of Ultradifferentiable Functions of Roumieu Type

Archiv Der Mathematik, 1988
Let \(K\subset {\mathbb{R}}^ n\) be a compact convex set and let \(E_{\{M_ j\}}(K)\) denote the ultradifferentiable functions of Roumieu type on K. It is shown, that there is no continuous linear extension operator \(T: E_{\{M_ j\}}(K)\to E_{\{M_ j\}}(J)\), if the sequence \((M_ j)\) is regular (\(K\subset\overset\circ J\subset {\mathbb{R}}^ n)\). This
Michael Langenbruch
exaly   +3 more sources

Continuation of functionals on ultradifferentiable function spaces

Analysis Mathematica, 1995
The paper generalizes a few results of \textit{M. A. Solov'ev} [Theor. Math. Phys. 15, 317-328 (1974; Zbl 0273.46030)] and adds further results in line with the first author's work on the subject. The Fourier-Laplace transform of functionals defined on the spaces \(Sa^q_k\) are considered. It may be mentioned here that \textit{J. M. C.
Pathak, R. S., Paul, A. C.
openaire   +2 more sources

Ultradifferentiable Functions on Compact Intervals

Mathematische Nachrichten, 1989
The author deals with finding the spaces of ultradifferentiable functions which are linear topologically isomorphic to a power series space. The problem is treated for the spaces \({\mathcal E}_{(M_ p)}(I)\) (and \({\mathcal E}_{\{M_ p\}}(I))\) of all ultradifferentiable functions of the Beurling type (resp.
openaire   +1 more source

Weight Functions for Classes of Ultradifferentiable Functions

Results in Mathematics, 1994
\textit{A. Beurling} [Lectures 4 and 5, AMS Summer Institute, Stanford (1961)] has used subadditive weight functions \(\omega\) to define non- quasianalytic classes of ultradifferentiable functions \({\mathcal E}_{(\omega)} (\mathbb{R})\). Some authors also have defined different weight functions for the classes \({\mathcal E}_{(\omega)} (\mathbb{R})\).
exaly   +2 more sources

Ultradifferentiable functions and Fourier analysis

Results in Mathematics, 1990
In Beurling's approach to ultradifferentiable functions, decay properties of the Fourier transform of the functions are imposed rather than growth conditions on the derivatives, as it has been done classically. In the present article the authors modify Beurling's approach. They define for nonempty open subsets \(\Omega\) of \(\mathbb{R}^ N\) the spaces
Braun, R. W., Meise, R., Taylor, B. A.
openaire   +2 more sources

The Cauchy and Poisson kernels as ultradifferentiable functions

Complex Variables, 1998
Let C be an open convex cone in such that does not contain any entire straight line. We previously have shown that the Cauchy and Poisson kernel functions corresponding to the tube are elements of the ultradifferentiable function spaces , where ∗ is either (Mp ) or {Mp }.
Richard D. Carmichael, S. Pilipović
openaire   +2 more sources

On the Moment Problem in the Spaces of Ultradifferentiable Functions of Mean Type

Siberian Mathematical Journal, 2022
The author studies the image of the Borel map \[ \rho:C^\infty(\mathbb{R}) \rightarrow \mathbb{C}^\mathbb{N}, \quad f \mapsto (f^{(n)}(0))_n \] restricted to spaces of ultradifferentiable functions of mean type as introduced in [\textit{D. A. Abanina}, Result. Math. 44, No. 3--4, 195--213 (2003; Zbl 1057.46025)].
exaly   +3 more sources