5 papers
Sufficient Conditions for Strong Natural Boundaries involving Lacunary Sequences
Rafael Reno S. Cantuba
The notion of a regular point is extended to that of a weak regular point, and so the notion of a strong natural boundary may be described locally as the absence of weak regular po…
A Kronecker-Weyl Theorem from Interpolation Sets
Rafael Reno S. Cantuba
An analog of the classical Kronecker-Weyl theorem for weak uniform distribution is obtained for an arbitrary countably infinite independent subset of a discrete abelian group using…
Five Circles: Real Analysis Theorems equivalent to Completeness
Rafael Cantuba
This is an exposition of the work of O. Riemenschneider about five ''circles'' of implications relating real analysis theorems each equivalent to the Dedekind completeness of the r…
Compactness Arguments in Real Analysis
Rafael Cantuba
Theorems crucial in elementary real function theory have proofs in which compactness arguments are used. Despite the introduction in relatively recent literature of each new highly…
Lie polynomials in a -deformed universal enveloping algebra of a low-dimensional Lie algebra
Rafael Reno S. Cantuba, Mark Anthony C. Merciales
The nonabelian two-dimensional Lie algebra over a field has a presentation by generators , and relation , with the universal enveloping alg…