A wavelet, in the generalized sense, is a vector in the Hilbert space, Hπ , of a unitary representation, π, of a locally compact group, G, with the property that the wavelet transform it defines is an isometry of Hπ into L2(G). We study the image of this transform and how that image varies as the wavelet varies. We obtain a version of the Peter-Weyl Theorem for the class of groups for which the...

A characterization of the space L2[−σ, σ] in terms of its image under the Fourier transformation has been given by the Paley-Wiener theorem [5]. The theorem asserts that f ∈ L2[−σ, σ] if and only if its Fourier transform f̂(ω) can be continued analytically to the whole complex plane as an entire function of exponential type at most σ whose restriction to the real axis belongs to L2(R). This char...

Some estimates are proved for the generalized Fourier-Bessel transform in the space (L^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

to enrich our understanding of the attitudinal/motivational basis of foreign language learning at junior high school level, this study investigated the students’ status of l2 motivation, the relationship between motivational factors, and the possibility of predicting their motivated learning behavior in light of dörnyei’s (2005, 2009) theory of l2 motivational self system. to this end, 1462 jun...

We consider the phase retrieval problem in which one tries to reconstruct a function from the modulus of its wavelet transform. We study the unicity and stability of the reconstruction. In the case where the wavelets are Cauchy wavelets, we prove that the modulus of the wavelet transform uniquely determines the function up to a global phase. We show that the reconstruction operator is continuou...

Image compression is an application of data compression on digital images, which is in high demand as it reduces the computational time and consequently the cost in image storage and transmission. The basis for image compression is to remove redundant and unimportant data while to keep the compressed image quality in an acceptable range. In this work, Fast Fourier Transform (FFT), Discrete Cosi...

M. Lacey and C. Thiele proved in [26] (Annals of Math. (1997)) and [27] (Annals of Math. (1999)) that the bilinear Hilbert transform maps L1 × L2 → L boundedly when 1 p1 + 1 p2 = 1 p with 1 < p1, p2 ≤ ∞ and 2 3 < p < ∞. Whether the L estimates hold in the range p ∈ (1/2, 2/3] has remained an open problem since then. In this paper, we prove that the bilinear Hilbert transform does not satisfy an...

Since its appearing in 1996 [2], the Stockwell transform (S-transform) has been used as a tool in medical imaging, geophysics and signal processing in general. In this talk, we prove that the system of functions (so-called DOST basis), introduced by R. Stockwell in [3], is indeed an orthonormal basis of L2([0, 1]), which is a time-frequency localized basis, in the sense of Donoh-Stark Theorem [...

This paper deals with the construction of biorthogonal p -wavelet packets on R+ related to the Walsh polynomials and their properties are investigated by means of Walsh-Fourier transform. Three biorthogonal formulas regarding these p -wavelet packets are derived. Moreover, it is shown how to obtain several new Riesz bases of the space L2(R+) by constructing a series of subspaces of these p -wav...

The concept of vector-valued multiresolution analysis on local field of positive characteristic was considered by Abdullah [Vector-valued multiresolution analysis on local fields of positive characteristic, Analysis. 34(2014) 415-428]. We construct the associated wavelet packets for such an MRA and investigate their properties by virtue of the Fourier transform. Moreover, it is shown how to obt...