The compact Hausdorff space X has the Complex Stone-Weierstrass Property (CSWP) iff it satisfies the complex version of the Stone-Weierstrass Theorem. W. Rudin showed that all scattered spaces have the CSWP. We describe some techniques for proving that certain non-scattered spaces have the CSWP. In particular, if X is the product of a compact ordered space and a compact scattered space, then X ...

Let X denote a compact Riemann surface of genus g > 1. At each point P~X, there is a sequence of g integers, l=71(P)<72(P)<. . .<Tg(P)<2g , called the Weierstrass gap sequence at P. A positive integer ~/is a Weierstrass gap at P if there exists a holomorphic differential on X with a zero of order 7 1 at P. A positive integer which is not a gap at P is called a nongap at P. The point P is called...

The group generated by the Weierstrass points of a smooth curve in its Jacobian is an intrinsic invariant of the curve. We determine this group for all smooth quartics with eight hyperflexes or more. Since Weierstrass points are closely related to moduli spaces of curves, as an application, we get bounds on both the rank and the torsion part of this group for a generic quartic having a fixed nu...

The Stone-Weierstrass Theorem for compact Hausdorff spaces is a basic result of functional analysis with far-reaching consequences. We introduce an equational logic ? ? associated infinitary variety and show that the consequence Beth definability property , stating every implicit definition can be made explicit. Further, we define propositional ? by means Hilbert-style calculus prove strong com...

Abstract In this note, we spotlight a generalization of Weierstrass integral operators introduced by Eugeniusz Wachnicki. The construction involves modified Bessel functions. are correlated with diffusion equation. Our main result consists in obtaining the asymptotic expansion derivatives any order Wachnicki’s operators. All coefficients explicitly calculated, and distinct expressions provided ...