13 citations · 46 across the 16 of their papers we have counts for
18 papers
Zero Harmonic Density implies Zero Density
Rafael Reno S. Cantuba
A set of integers has zero harmonic density if its elements, viewed as frequencies of continuous characters of the unit circle as a compact group, are measure-theoretically sparse…
Extension Theorems in Measure and Integration Theory as Completeness Axioms
Rafael Reno S. Cantuba
In measure and integration theory, the themes of extending premeasures to outer measures and extending Daniell linear functionals to Daniell integrals are governed by the foundatio…
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…
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…
Littlewood's principles in reverse real analysis
Rafael Reno S. Cantuba
If local forms of Littlewood's three principles are stated as axioms for an ordered field, then each principle is equivalent to the completeness axiom.
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 structure of the Heisenberg-Weyl algebra
Rafael Reno S. Cantuba
As an associative algebra, the Heisenberg-Weyl algebra is generated by two elements , subject to the relation . As a Lie algebra, however, where the u…
Extended commutator algebra for the -oscillator and a related Askey-Wilson algebra
Rafael Reno S. Cantuba
Let be a nonzero complex number that is not a root of unity. In the -oscillator with commutation relation , it is known that the smallest commutator algebr…
Ubiquitous Lie polynomials in a two-generator universal enveloping algebra
Rafael Reno S. Cantuba
The universal enveloping algebra of a two-dimensional nonabelian Lie algebra is a Lie algebra itself with the commutator as Lie bracket. There exists a presentati…
Torsion-type -deformed Heisenberg algebra and its Lie polynomials
Rafael Reno S. Cantuba, Sergei Silvestrov
Given a scalar parameter , the -deformed Heisenberg algebra is the unital associative algebra with two generators that satisfy the -deformed commuta…
An extension of a -deformed Heisenberg algebra and its Lie polynomials
Rafael Reno S. Cantuba, Mark Anthony C. Merciales
Let be a field, and fix a . The -deformed Heisenberg algebra is the unital associative algebra over with generators $A…
Lie polynomials in an algebra defined by a linearly twisted commutation relation
Rafael Reno S. Cantuba
We present an elementary approach in characterizing Lie polynomials in the generators of an algebra with a defining relation that is in the form of a deformed or twisted comm…
A Casimir element inexpressible as a Lie polynomial
Rafael Reno S. Cantuba
Let be a scalar that is not a root of unity. We show that any polynomial in the Casimir element of the Fairlie-Odesskii algebra cannot be expressed in t…
A -deformed Heisenberg algebra as a normed space
Rafael Reno S. Cantuba
Given a real number such that , the natural setting for the mathematics of a -oscillator is an infinite-dimensional, separable Hilbert space that is said to provide a…
Lie polynomials in -deformed Heisenberg algebras
Rafael Reno S. Cantuba
Let be a field, and let . The -deformed Heisenberg algebra is the unital associative -algebra with generators and…
A Lie algebra related to the universal Askey-Wilson algebra
Rafael Reno S. Cantuba
Let denote an algebraically closed field. Denote the three-element set by , and let denote the free unital…