The multidimensional Jackson theorem

TL;DR: The theory of persistence modules is an emerging field of algebraic topology which originated in topological data analysis as discussed by the authors, and has been applied to a wide range of applications in algebraic and differential topology.

TL;DR: A new lower bound for the cardinality of spherical designs was obtained in this paper, which improved the well-known bound of Delsarte by an exponential factor as the degree of the design tends to infinity.

TL;DR: In this paper, the Fourier-Laplace series on a k-dimensional (k ≥ 3) sphere was studied and the results which are presently known in the theory of Fourier Laplace series were presented.

TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.

TL;DR: The tabulation of Bessel functions can be found in this article, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.

Abstract: 1. Bessel functions before 1826 2. The Bessel coefficients 3. Bessel functions 4. Differential equations 5. Miscellaneous properties of Bessel functions 6. Integral representations of Bessel functions 7. Asymptotic expansions of Bessel functions 8. Bessel functions of large order 9. Polynomials associated with Bessel functions 10. Functions associated with Bessel functions 11. Addition theorems 12. Definite integrals 13. Infinitive integrals 14. Multiple integrals 15. The zeros of Bessel functions 16. Neumann series and Lommel's functions of two variables 17. Kapteyn series 18. Series of Fourier-Bessel and Dini 19. Schlomlich series 20. The tabulation of Bessel functions Tables of Bessel functions Bibliography Indices.

TL;DR: In this paper, the authors present a generalization of the trigonometric interpolation polynomial of Lagrange to a function of exponential type and show that the resulting function can be represented as a linear space.