Isoperimetric Sandwiches and Approximation by Analytic and Harmonic Functions

1. Auflage 2021
ISBN: 978-1-4987-5636-5
Verlag: Taylor & Francis Inc

Buch, Englisch, 304 Seiten, Format (B × H): 156 mm x 234 mm

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

The book focuses on a number of results and open problems dealing with a wide variety of isoperimetric inequalities., this approach can be characterized by a recently coined term "sandwiches". A certain quantity is introduced, usually as a degree of approximation to a given simple function, e.g., z*, x ^2, by either analytic or harmonic functions in some norm. Then, the estimates from below and above of the approximate distance are obtained in terms of simple geometric characteristics of the set, e.g., area, perimeter, capacity, etc. The resulting "sandwich" yields the isoperimetric inequality.

Autoren/Hrsg.

Beneteau, Catherine

Khavinson, Dmitry

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Introduction. Analytic content in Smirnov and Bergman norms. Toeplitz operators, isoperimetric inequalities, Bergman orthogonal polynomials. Higher dimensions: harmonic approximation and isoperimetric inequalities. Other free boundary problems in two dimensions. Concluding Remarks

Über Autor(innen)

Catherine Bénéteau is an Associate Professor at the University of South Florida. She has secured numerous grants and awards for her work, and organised many conferences and workshops. She is a Referee for several top journals including Complex Analysis and Operator Theory, Complex Variables and Elliptic Equations, Computational Methods and Function Theory. Dmitry Khavinson is a Distinguished University Professor, University of South Florida. With a long history of high quality publications in this area, he is an established authority in this field. He has been awarded numerous grants and awards for his work including the 2015 USF Outstanding Faculty Achievement Award.