On Zemanian's distributional eigenfunction transforms

Combined Eigenfunction Expansion and Convergence Accelerator Approach to the Rapid Numerical Evaluation of Hilbert Transforms

The numerical evaluation of a class of Hilbert transforms using an eigenfunction approach is considered. Judicious selection of convergence accelerators allows for the efficient evaluation of the resulting series. The approach is particularly accurate for functions having a Gaussian-like asymptotic behavior. For more slowly decreasing functions, the accuracy of the evaluation decreases.

On the multiplicative products of the n-dimensional distributional Hankel transforms

I. abstract. In this note, we prove several multiplicative products of the n-dimensional Hankel transform. In fact the following formulae: H{δ (k) (u(x))}.H{δ () (u(x))} = DH δ (k++ n−2 2) (u(x)) , (III,1)

On ∆ - Transforms

Any set of two legs in a Gough–Stewart platform sharing an attachment is defined as a ∆component. This component links a point in the platform (base) to a line in the base (platform). Thus, if the two legs, which are involved in a ∆ component, are rearranged without altering the location of the line and the point in their base and platform local reference frames, the singularity locus of the Go...

Perturbation of eigenfunction expansions.

Convergence of Generalized Eigenfunction Expansions

We present a simplified theory of generalized eigenfunction expansions for a commuting family of bounded operators and with finitely many unbounded operators. We also study the convergence of these expansions, giving an abstract type of uniform convergence result, and illustrate the theory by giving two examples: The Fourier transform on Hecke operators, and the Laplacian operators in hyperboli...