This paper aims to study the q-wavelet and the q-wavelet transforms, associated with the q-Bessel operator for a fix q ∈]0, 1[. As application, an inversion formulas of the q-Riemann-Liouville and q-Weyl transforms using q-wavelets are given. For this purpose, we shall attempt to extend the classical theory by giving their q-analogues.

We establish the inverse Lebedev expansion with respect to parameters and arguments of the modified Bessel functions for an arbitrary function from Hardy’s space H2,A, A> 0. This gives another version of the Fourier-integral-type theorem for the Lebedev transform. The result is generalized for a weighted Hardy space Ĥ2,A ≡ Ĥ2((−A,A);|Γ(1+Rez+iτ)|2dτ), 0 < A < 1, of analytic functions f(z),z = R...

In this paper a novel modeling technique for speech signals, based on the source-filter model of speech production and on orthogonal transform theory, is presented. The proposed approach models the impulse response of such filter, by projection onto a basis of damped Bessel functions, which have been chosen for their similarity to the signal to be modeled. In such a way an orthogonal transform ...

This paper extends the Meijer transformation, M, given by I /2K 2p f(t) (pt) (2 p)dt, (Mf) (p) (i+) 0 where f belongs to an appropriate function space, e (-1,) and K is the modified Bessel function of third kind of order , to certain generalized functions. A testing space is constructed so as to contain the (pt)/2K(2p), of the transformation. Some properties of the kernel, function space and it...

A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined Fourier–Bessel series transforms, respectively. Their equivalent relation shown, which the upper bound estimate for best RKHS provided. The convergence rate bounded modulus smoothness, shows that can attain sa...

In this paper, we prove two estimates useful in applications for the Fourier-Bessel transform space Lp(R2+,x2?1+1y2?2+1dxdy), (1 &lt; p ? 2), as applied to some classes of functions characterized by a generalized modulus continuity.

&lt;p style='text-indent:20px;'&gt;In this article, we have investigated certain definite integrals and various integral transforms of the generalized multi-index Bessel function, such as Euler transform, Laplace Whittaker K-transform Fourier transforms. Also found applications problem on fractional kinetic equation pertaining to function using Sumudu transform technique. Mittage-Leffler is use...

We obtain representations for the Mellin transform of the product of generalized hypergeometric functions 0 F1[ ax]1 F2[ b2x2] for a;b > 0. The later transform is a generalization of the discontinuous integral of Weber and Schafheitlin; in addition to reducing to other known integrals (for example, integrals involving products of powers, Bessel and Lommel functions), it contains numerous integr...

In this paper, the quaternion Bessel-Fourier moments are introduced. The significance of phase information in quaternion Bessel-Fourier moments is investigated and an accurate estimation method for rotation angle is described. Furthermore, a new set of invariant descriptors based on the magnitude and the phase information of quaternion Bessel-Fourier moments is derived. Experimental results sho...

A new method for analysis of electroencephalogram (EEG) signals using Empirical Mode Decomposition (EMD) and Fourier-Bessel (FB) expansion has been presented in this paper. The EMD decomposes a EEG signal into a finite set of band-limited signals termed Intrinsic Mode Functions (IMFs). The mean frequency (MF) for each IMF has been computed using FB expansion. The MF measure of the IMFs has been...