Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

The coherent states associated to the discrete series representations D(Eo, s) of SO(3, 2) are constructed in terms of (spin-)tensor fields on D = 4 anti-de Sitter space. For Eo > s + 5 the linear space HEo,s spanned by these states is proved to carry the unitary irreducible representation D(Eo, s). The SO(3, 2)-covariant generalized Fourier transform in this space is exhibited. The quasiclassi...

We elucidate the relation between the two ways of formulating causality in nonlocal quantum field theory: using analytic test functions belonging to the space S (which is the Fourier transform of the Schwartz space D) and using test functions in the Gelfand-Shilov spaces S α. We prove that every functional defined on S 0 has the same carrier cones as its restrictions to the smaller spaces S α. ...

The coherent states associated to the discrete series representations D(E o , s) of SO(3, 2) are constructed in terms of (spin-)tensor fields on D = 4 anti-de Sitter space. For E o > s + 5 the linear space H Eo,s spanned by these states is proved to carry the unitary irreducible representation D(E o , s). The SO(3, 2)-covariant generalized Fourier transform in this space is exhibited. The quasi...

Using a generalized translation operator, we obtain a generalization of Theorem 5 in [4] for the Bessel transform for functions satisfying the (delta;gamma ; 2)-BesselLipschitz condition in L_{2;alpha}(R+).  

in general, energy prices, such as those of crude oil, are affected by deterministic events such as seasonal changes as well as non-deterministic events such as geopolitical events. it is the non-deterministic events which cause the prices to vary randomly and makes price prediction a difficult task. one could argue that these random changes act like noise which effects the deterministic variat...

We extend the functional analytic approach to Colombeautype spaces of nonlinear generalized functions in order to study algebras of tempered generalized functions. We obtain a definition of Fourier transform of nonlinear generalized functions which has a strict inversion theorem, agrees with the classical Fourier transform for tempered distributions and preserves well-known classical properties...