A Fast Transform for Spherical Harmonics.
A multiplier theorem for ultraspherical series
A new form of the spherical expansion of zonal functions and Fourier transforms of -finite functions.
A new perspective on some approximations used in neutron transport modeling
In this contribution, we will use the Maxwell-Cartesian spherical harmonics (introduced in [1,2]) to derive a system of partial differential equations governing transport of neutrons within an interacting medium. This system forms an alternative to the well known approximation, which is based on the expansion of the directional dependence into tesseral spherical harmonics ([3,p.197]). In comparison with this latter set of equations, the Maxwell-Cartesian system posesses a much more regular structure,...
A note on certain classes of transformation formulas involving several variables.
A note on semi-classical orthogonal polynomials.
A radial derivative with boundary values of the spherical Poisson integral.
A solution of the boundary value problem in heat conduction
Allied integrals, functions, and series for the unit sphere.
An Addition Theorem for Some q-Hahn Polynomials.
An operational formula involving the associated ultraspherical polynomials
Analogues of Besicovitch-Wiener Theorem for Heisenberg Group.
Arbitrary complex powers of the Dirac operator on the hyperbolic unit ball.
Bilateral generating functions for a new class of generalized Legendre polynomials.
Certain formulas associated with generalized Rice polynomials, II
Cube Groups Invariant Spherical Harmonics and Krawtchouk Polynomials.
Curriculum vita of Prof. Vasil Atanasov Popov
Our primary goal in this preamble is to highlight the best of Vasil Popov’s mathematical achievements and ideas. V. Popov showed his extraordinary talent for mathematics in his early papers in the (typically Bulgarian) area of approximation in the Hausdorff metric. His results in this area are very well presented in the monograph of his advisor Bl. Sendov, “Hausdorff Approximation”.
Differential operators of gradient type associated with spherical harmonics
Discrete approximation of the solution of the Dirichlet problem by discrete means.
Distributions of truncations of the heat kernel on the complex projective space
Let be a Brownian motion valued in the complex projective space . Using unitary spherical harmonics of homogeneous degree zero, we derive the densities of and of , and express them through Jacobi polynomials in the simplices of and respectively. More generally, the distribution of may be derived using the decomposition of the unitary spherical harmonics under the action of the unitary group yet computations become tedious. We also revisit the approach initiated in [13] and based on...