We establish the various relationships that exist among the integral transform Ᏺ α,β F , the convolution product (F * G) α , and the first variation δF for a class of functionals defined on K[0,T ], the space of complex-valued continuous functions on [0,T ] which vanish at zero. 1. Introduction and definitions. In a unifying paper [10], Lee defined an integral transform Ᏺ α,β of analytic functi...

Multilevel algorithms developed for the fast evaluation of integral transforms and the solution of the corresponding integral and integro-diierentialequations rely on smoothnessproperties of the discrete kernel (matrix) and thereby on grid uniformity (see 6], 18]). However, in actual applications, e.g. in contact mechanics, in many cases a substantial increase of eeciency can be obtained using ...

We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.

Most standard fractal image compression techniques rely on using an IFS operator directly on the image function. Sometimes, however , it is more convenient to work on a faithful representation of the image which, in certain applications, may be a transformed version of the image. For example, if an MRI image is scanned in as frequency data it may be more natural to work on the Fourier transform...

By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, the Christoffel-Darboux-type bilinear generating function and their asymptotic expressions, we obtain quadrature formulas for integral transforms generated by the classical orthogonal polynomials. These integral transforms, related to the so-called Poisson integrals, correspond to a modified Fourier Tra...

The known integral transforms of Funk-Radon type are applied 5 to manifolds which have algebraic structure (planes, spheres, ellipsoids, hyper6 boloids, paraboloids etc.). A variety of new exact reconstructions is described 7 in this paper for the integral transforms on arbitrary smooth manifolds X 8 embedded in an a¢ ne space E with an additional structure. 9 MSC (2010) Primary 53C65; Secondar...

The Gaussian scale-space is a singular integral convolution operator with scaled Gaussian kernel. For a large class of singular integral convolution operators with differentiable kernels, a general method for constructing mother wavelets for continuous wavelet transforms is developed, and Calderón type inversion formulas, in both integral and semi-discrete forms, are derived for functions in L ...

The paper describes an approach to dynamic multivariate analysis in which principal component analysis (PCA) is combined with integral transform techniques. The aim was to detect correlations when process dynamics cause lags or time delays. The techniques give a signature that characterises the correlated measurements. Tools for Fourier and wavelet PCA have been developed and tested. They have ...

We introduce a class of stochastic differential equations driven by fractional Brownian motion (FBM), which allow for a constructive method in order to obtain stationary solutions. This leads to a substantial extention of fractional Ornstein-Uhlenbeck processes. Structural properties of this class of new models are investigated. Their stationary densities are given explicitly. Short title: Frac...