We have showed previously that the Fourier transform is an isometric isomorphism on L2 = CcR ∩ L2Rn. In particular, we have a ∀u ∈ L2 ||u||0 = ||û||0 Parseval relation b ∀u,v ∈ L2, u,v0 = û, v̂0 Plancherel relation The results (a) and (b) hold for every test function, and since the test functions are dense in L2Rn, they extend to L2Rn by continuity. Then the Fourier transform can...

in this paper, using a generalized translation operator, we prove theestimates for the generalized fourier-bessel transform in the space l2 on certainclasses of functions.

This paper constructs translation-invariant operators on L2.Rd /, which are Lipschitz-continuous to the action of diffeomorphisms. A scattering propagator is a path-ordered product of nonlinear and noncommuting operators, each of which computes the modulus of a wavelet transform. A local integration defines a windowed scattering transform, which is proved to be Lipschitz-continuous to the actio...

Critical pedagogy (CP) empowers L2 learners to have a voice in the classroom and in the society. This study was an attempt to investigate whether the current classroom discourse  in  Iran  can  endow  the  L2  learners with  a  critical  awareness  to  actively transform their learning processes and creatively engage in collaborative dialogues to construct new knowledge. To this end, the discou...

critical pedagogy (cp) empowers l2 learners to have a voice in the classroom and in the society. this study was an attempt to investigate whether the current classroom discourse  in  iran  can  endow  the  l2  learners with  a  critical  awareness  to  actively transform their learning processes and creatively engage in collaborative dialogues to construct new knowledge. to this end, the discou...

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

This paper is devoted to embedding theorems for the space Kθ, where θ is an inner function in the unit disc D. As we will see soon, the question of embedding of Kθ into L2(μ) is virtually equivalent to the boundedness of two-weight Hilbert transform. This makes the embedding question quite difficult (the general bondedness criteria of Hunt-Muckenhoupt-Wheeden type for two weight Hilbert transfo...

In the present paper, the authors introduce identities for the L2-transform which yield a Parseval type relationship for the L2-transform. The Parseval type relationship proven in this paper give rise to useful corollaries for evaluating indefinite integrals of special functions. Some examples are also given as illustrations of the results presented here. ! 2007 Elsevier Inc. All rights reserved.

in hilbert space l2(rn), we prove the equivalence between the mod-ulus of smoothness and the k-functionals constructed by the sobolev space cor-responding to the fourier transform. for this purpose, using a spherical meanoperator.