If H denotes the classical Hilbert transform and Hu(x) = v(x), then the functions u(x) and v(x) are the values on the real axis of a pair of conjugate functions, harmonic in the upper half-plane. This note gives a generalization of the above concepts in which the Laplace equation Deltau = 0 is replaced by the Yukawa equation Deltau = mu(2)u and in which the Cauchy-Riemann equations have a corre...

Fourier transform can be generalized into the fractional Fourier transform (FRFT), linear canonical transform (LCT), and simplified fractional Fourier transform (SFRFT). They extend the utilities of original Fourier transform, and can solve many problems that can’t be solved well by original Fourier transform. In this paper, we will generalize the cosine transform. We will derive fractional cos...

Our objective in this survey is to present some results concerning to transference of multipliers, maximal multipliers and transplantation operators between Fourier-Bessel series and Hankel integrals. Also we list some related problems that can be interesting and that have not been studied yet. From August 31st to September 3rd, 2004, was held in Merlo (San Luis, Argentine) the congress ”VII En...

In this paper, we define Sobolev spaces on a locally compact unimodular group in link with the spherical Fourier transform of type $\delta$. Properties these are obtained. Analogues embedding theorems proved.

The method of superposition and separation variables is applied to gain analytical solutions to the transient heat conduction for a two dimensional cylindrical fin. The temperature distributions are generalized for a linear combination of the product of Bessel function, Fourier series and exponential type for nine different cases. The solutions presented in this study can be used to verify the ...

In a two-dimensional pattern matching problem, a known template image has be located in another image, irrespective of the template's position, orientation and size in the image. One way to accomplish invariance to the changes in the template is by forming a set of feature vectors that encompass all the variations in the template. Matching is then performed by finding the best similarity betwee...

In this paper, a signal processing framework in a generalized Fourier domain (GFD) is introduced. In this newly proposed domain, a parametric form of control on the periodic repetitions that occur due to sampling in the reciprocal domain is possible, without the need to increase the sampling rate. This characteristic and the connections of the generalized Fourier transform to analyticity and to...