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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis

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Fatou Type Theorems - Maximal Functions and Approach Regions (Paperback, 1998 ed.) Loot Price: R1,856
Discovery Miles 18 560
Fatou Type Theorems - Maximal Functions and Approach Regions (Paperback, 1998 ed.): F. Di Biase
Fatou Type Theorems - Maximal Functions and Approach Regions (Paperback, 1998 ed.): F. Di Biase

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Fatou Type Theorems - Maximal Functions and Approach Regions (Paperback, 1998 ed.)

F. Di Biase

Series: Progress in Mathematics, 147

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Loot Price R1,856 Discovery Miles 18 560 | Repayment Terms: R172 pm x 12*

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A basic principle governing the boundary behaviour of holomorphic func- tions (and harmonic functions) is this: Under certain growth conditions, for almost every point in the boundary of the domain, these functions ad- mit a boundary limit, if we approach the bounda-ry point within certain approach regions. For example, for bounded harmonic functions in the open unit disc, the natural approach regions are nontangential triangles with one vertex in the boundary point, and entirely contained in the disc [Fat06]. In fact, these natural approach regions are optimal, in the sense that convergence will fail if we approach the boundary inside larger regions, having a higher order of contact with the boundary. The first theorem of this sort is due to J. E. Littlewood [Lit27], who proved that if we replace a nontangential region with the rotates of any fixed tangential curve, then convergence fails. In 1984, A. Nagel and E. M. Stein proved that in Euclidean half- spaces (and the unit disc) there are in effect regions of convergence that are not nontangential: These larger approach regions contain tangential sequences (as opposed to tangential curves). The phenomenon discovered by Nagel and Stein indicates that the boundary behaviour of ho)omor- phic functions (and harmonic functions), in theorems of Fatou type, is regulated by a second principle, which predicts the existence of regions of convergence that are sequentially larger than the natural ones.

General

Imprint: Springer-Verlag New York
Country of origin: United States
Series: Progress in Mathematics, 147
Release date: 2012
First published: 1998
Authors: F. Di Biase
Dimensions: 235 x 155 x 9mm (L x W x T)
Format: Paperback
Pages: 154
Edition: 1998 ed.
ISBN-13: 978-1-4612-7496-4
Barcode: 9781461274964
Categories: Promotions
Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
LSN: 1-4612-7496-6

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