Results 41 to 50 of about 370 (125)

Structure Theorem for Functionals in the Space 𝔖ω1,ω2′

International Journal of Mathematics and Mathematical Sciences, Volume 2008, Issue 1, 2008., 2008
We introduce the space 𝔖ω1,ω2 of all C∞ functions ϕ such that sup|α|≤m∥ekω1∂αϕ∥∞ and sup|α|≤m∥ekω2∂αϕ∧∥∞ are finite for all k ∈ ℕ0, α∈ℕ0n, where ω1 and ω2 are two weights satisfying the classical Beurling conditions. Moreover, we give a topological characterization of the space 𝔖ω1,ω2 without conditions on the derivatives.
Hamed M. Obiedat, Wasfi A. Shatanawi, Mohd M. Yasein, Manfred H. Moller   +3 more
wiley   +1 more source

Multipliers and operators on the tempered ultradistribution spaces of Roumieu type for the distributional Hankel‐type transformation spaces

International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006
The tempered ultradistribution space of Roumieu type for the space Hμ,ν is defined, which is a subspace of the Hausdörff locally convex topological linear space. Further, results are obtained for the multipliers and operators on the tempered ultradistribution spaces for the distributional Hankel‐type transformation spaces.
P. K. Banerji, S. K. Al-Omari
wiley   +1 more source

Convolution of n-dimensional Tempered Ultradistributions and Field Theory [PDF]

, 2022
In this work, a general definition of convolution between two arbitrary Tempered Ultradistributions is given. When one of the Tempered Ultradistributions is rapidly decreasing this definition coincides with the definition of J. Sebastiao e Silva.
Rocca, Mario Carlos, Bollini, Carlos Guido   +1 more
core  

On the Fourier transform and the exchange property

International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 16, Page 2579-2584, 2005., 2005
A simplified construction of tempered Boehmians is presented. The new construction shows that considering delta sequences and convergence arguments is not essential.
Dragu Atanasiu, Piotr Mikusiński
wiley   +1 more source

The characterization of the almost periodic ultradistributions of Beurling type [PDF]

, 1992
We introduce and study the space of almost periodic ultradistributions of Beurling type and characterize it in terms of classical Bohr almost periodicity. To this aim we establish a structure theorem for the bounded ultradistributions.
Ioana Cioranescu
core   +1 more source

Asymptotic hyperfunctions, tempered hyperfunctions, and asymptotic expansions

International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 5, Page 755-788, 2005., 2005
We introduce new subclasses of Fourier hyperfunctions of mixed type, satisfying polynomial growth conditions at infinity, and develop their sheaf and duality theory. We use Fourier transformation and duality to examine relations of these asymptotic and tempered hyperfunctions to known classes of test functions and distributions, especially the Gel′fand‐
Andreas U. Schmidt
wiley   +1 more source

The kernel theorem for Cauchy ultradistribution

Journal of Mathematical Analysis and Applications, 2003
Because of the popularity currently gained by ultradistribution theory (after the heydays of Schwartz distribution theory) the authors have tried to extend the results concerning kernel theorems to ultradistributions. Some elementary results are proved under the heading ``The kernel theorem''.
Banerji, P.K., Debnath, Lokenath, Bhandari, Deshna   +2 more
openaire   +1 more source

Spaces of Test Functions via the STFT

Journal of Function Spaces, Volume 2, Issue 1, Page 25-53, 2004., 2004
We characterize several classes of test functions, among them Björck′s ultra‐rapidly decaying test functions and the Gelfand‐Shilov spaces of type S, in terms of the decay of their short‐time Fourier transform and in terms of their Gabor coefficients.
Karlheinz Gröchenig, Georg Zimmermann, Hans Feichtinger   +2 more
wiley   +1 more source

Polynomials on the space of ω-ultradifferentiable functions [PDF]

Opuscula Mathematica, 2007
The space of polynomials on the the space \(D_{\omega}\) of \(\omega\)-ultradifferentiable functions is represented as the direct sum of completions of symmetric tensor powers of \(D^{\prime}_{\omega}\).
Katarzyna Grasela
doaj  

Wavelet transforms in generalized Fock spaces

International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 657-672, 1997., 1996
A generalized Fock space is introduced as it was developed by Schmeelk [1‐5], also Schmeelk and Takači [6‐8]. The wavelet transform is then extended to this generalized Fock space. Since each component of a generalized Fock functional is a generalized function, the wavelet transform acts upon the individual entry much the same as was developed by ...
John Schmeelk, Arpad Takači
wiley   +1 more source