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Articles by Stephan Ramon
Mathematics > Complex Variables
We prove that the Fermat equation $f^n+g^n=h^n$ with exponent $n\geq 4$ has no nontrivial solutions $f,g,h$ in the star-invariant subspace $K_θ^p$, in which $1\leq p\leq\infty$, whenever the boundary spectrum of the inner function $θ$ has logarithmic capacity zero. This gives a positive answer, for this class of inner functions and exponents, to a problem posed by Dyakonov.
Numerical semigroups from rational matrices IV: computation of the matricial dimensions of numerical semigroups with small Frobenius number or genus
arXiv:2510.15209 (math) View PDF HTML (experimental) Comments: Subjects: Combinatorics (math.CO) Cite as: arXiv:2510.15209 [math.CO] (or arXiv:2510.15209v1 [math.CO] for this version) https://doi.org/10.48550/arXiv.2510.15209 Submission history From: Stephan Garcia R [ view email] [v1] Fri, 17 Oct 2025 00:32:42 UTC (15 KB) Bibliographic Tools Bibliographic Explorer Toggle Bibliographic Explorer () Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps...
Partially isometric matrices: a brief and selective survey
Abstract We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also discuss the unitary similarity problem and several other results. Recommended Citation Garcia, Stephan, Mashreghi, Javad, and Ross, William T., "Model Spaces and Vector-Valued Nearly Invariant Subspaces." arXiv (March, 2019): 1-30.
[Description of] Operator Theory by Example
[Description of] Operator Theory by Example Description Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator.
the Pi Mu epsilon centennial collection
Title 100 years of math milestones : the Pi Mu epsilon centennial collection Author(s) Garcia, Stephan Ramon ; Miller, Steven J Publication Providence, RI : American Mathematical Society, 2019. - 597 p. Abstract This book is an outgrowth of a collection of 100 problems chosen to celebrate the 100th anniversary of the undergraduate math honor society Pi Mu Epsilon. Each chapter describes a problem or event, the progress made, and connections to entries from other years or other parts of mathematics.
"Approaching Cauchy’s Theorem" by Stephan Ramon Garcia and William T. Ross
Home > AS > Math and Computer Science > MATHCS-FACULTY-PUBLICATIONS > 219 Authors Stephan Ramon Garcia William T. Ross, University of RichmondFollow DOI 10.1080/10511970.2016.1234525 Abstract We hope to initiate a discussion about various methods for introducing Cauchy’s Theorem.
"Finite Blaschke Products and Their Connections" by Stephan Ramon Garcia, Javad Mashreghi et al.
Description This monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields. Old favorites such as the Carathéodory approximation and the Pick interpolation theorems are featured, as are many topics that have never received a modern treatment, such as the Bohr radius and Ritt's theorem on decomposability.
Introduction to model spaces and their operators
Home > Introduction to model spaces and their operators
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