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.
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Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Illustrationen
30 s/w Abbildungen
30 Illustrations, black and white
Maße
Höhe: 234 mm
Breite: 156 mm
ISBN-13
978-1-4987-5636-5 (9781498756365)
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Schweitzer Klassifikation
Catherine Beneteau 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.
Autor*in
University of South Florida, Tampa, USA
University of South Florida, Tampa, USA
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
