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English | 2024 | ISBN: 3985470723 | 148 Pages | True PDF | 16.6 MB [/center]
This work is devoted to the class of sets in the complex plane which are known as Carathéodory sets, more precisely as Carathéodory domains and Carathéodory compact sets. These sets naturally arose many times in various research areas in Real, Complex and Functional Analysis and in the Theory of Partial Differential Equations. For instance, the concept of a Carathéodory set plays a significant role in such topical themes as approximation in the complex plane, the theory of conformal mappings, boundary value problems for elliptic partial differential equations, etc. The first appearance of Carathéodory domains in the mathematical literature (of course, without the special name at that moment) was at the beginning of the 20th century, when C. Carathéodory published his famous series of papers about boundary behavior of conformal mappings. The next breakthrough result, which was obtained with the essential help of this concept, is the Walsh-Lebesgue criterion for uniform approximation of functions by harmonic polynomials on plane compacta (1929).
English | 2024 | ISBN: 3985470723 | 148 Pages | True PDF | 16.6 MB [/center]
This work is devoted to the class of sets in the complex plane which are known as Carathéodory sets, more precisely as Carathéodory domains and Carathéodory compact sets. These sets naturally arose many times in various research areas in Real, Complex and Functional Analysis and in the Theory of Partial Differential Equations. For instance, the concept of a Carathéodory set plays a significant role in such topical themes as approximation in the complex plane, the theory of conformal mappings, boundary value problems for elliptic partial differential equations, etc. The first appearance of Carathéodory domains in the mathematical literature (of course, without the special name at that moment) was at the beginning of the 20th century, when C. Carathéodory published his famous series of papers about boundary behavior of conformal mappings. The next breakthrough result, which was obtained with the essential help of this concept, is the Walsh-Lebesgue criterion for uniform approximation of functions by harmonic polynomials on plane compacta (1929).
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