Operator-Theoretic Approaches to Arithmetic Functional Analysis

Prime Numbers, Arithmetic Functions, Krein-Space Operators Under Free-Probabilistic Settings
1. Auflage 2027
ISBN: 978-1-041-37100-7
Verlag: Taylor & Francis Ltd

Buch, Englisch, 144 Seiten, Format (B × H): 156 mm x 234 mm

Reihe: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

This monograph explores the relationships and connections among number theory, operator theory, operator algebra theory, and representation theory within free-probabilistic frameworks. Arithmetic functions are examined as Krein-space operators under suitable representation, extending to free probability through the determination of point-evaluation linear functionals for primes.

Graduate students and researchers with interests in the aforementioned mathematical fields or related applied scientific areas will discover novel approaches to understanding these topics.

Understanding the images of arithmetic functions at primes as forms of matrices or operators acting Krein spaces will be of special interest to readers looking for new methods to analyse them mathematically.

Zielgruppe

Postgraduate

Autoren/Hrsg.

Cho, Ilwoo

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

1. Free-Probabilistic Structures Induced by Arithmetic Functions 2. Classifcations on Arithmetic Functions 3. Dirichlet Characters and Krein-Space Operators 4. Acting Arithmetic Functions on Matrices 5. Dynamical Systems of Arithmetic Functions Determined by Primes

Über Autor(innen)

Ilwoo Cho is a professor at Saint Ambrose University (Davenport, Iowa, USA). He got Ph.D. in Mathematics from University of Iowa in 2005. His main interests are free probability theory, operator algebra theory, operator theory, functional analysis including hypercomplex analysis.