4 papers · 1 filter
Multivariate Bessel functions and multivariate Hankel transforms
Victor G. Zakharov
The generalization, similarly to exponential multivariate bases in the Fourier transform, of the Bessel functions to many dimensions is offered. Analogously to the Fourier transfor…
Matrix method of polynomial solutions to constant coefficient PDE's
Victor G. Zakharov
In the paper, we introduce a matrix method to constructively determine spaces of polynomial solutions (in general, multiplied by exponentials) to a system of constant coefficient l…
Elliptic scaling functions as compactly supported multivariate analogs of the B-splines
Victor G. Zakharov
In the paper, we present a family of multivariate compactly supported scaling functions, which we call as elliptic scaling functions. The elliptic scaling functions are the convolu…
Polynomial spaces reproduced by elliptic scaling functions
Victor G. Zakharov
The Strang-Fix conditions are necessary and sufficient to reproduce spaces of algebraic polynomials up to some degree by integer shifts of compactly supported functions. W. Dahmen…