Generalization of Trigonometric B-splines and Kernels of Interpolating Trigonometric Splines with Riemann Convergence Multipliers

This paper explores the generalization of the method for extracting Riemann trigonometric B-splines and Riemann kernels of trigonometric interpolation splines of arbitrary order on different grids of stitching and interpolation. It is demonstrated that for various combinations of stitching and interpolation grids, distinct trigonometric B-splines exist. The theoretical principles are illustrated through a numerical example. The obtained results can have various practical applications.