The Langlands functoriality conjecture, as reformulated in the “beyond endoscopy” program, predicts comparisons between (stable) trace formulas of different groups G1,G2 for every morphism G1L→LG2 their L-groups. This conjecture can be seen a special case more general which replaces reductive by spherical varieties and formula its generalization, relative formula. goal this article continuation...

Chave presents an excellent algorithm and computer subprogram that evaluate Hankel transforms by quadrature and continued fraction summation. This subprogram would be a valuable addition to any mathematical computer library. Chave refers to digital filter (convolution) methods as “the standard numerical approach to the computation of Hankel transforms,” and makes numerous references to my publi...

The method of realizing certain self-reciprocal transforms as (absolute) scattering, previously presented in summarized form in the case of the Fourier cosine and sine transforms, is here applied to the self-reciprocal transform f(y) 7→ H(f)(x) = ∫∞ 0 J0(2 √ xy)f(y) dy, which is isometrically equivalent to the Hankel transform of order zero and is related to the functional equations of the Dede...

We discuss a fast approximate solution to the associated classical–classical orthogonal polynomial connection problem. first show that classical polynomials are solutions fourth-order quadratic eigenvalue problem with coefficients such differential operator is degree-preserving. Upon linearization, discretization of this block upper-triangular and banded. After perfect shuffle, we extend divide...