عنوان

Fatou Type Theorems

شابک

9781461223108

شابک

9781461274964

شماره

b402890

عنوان اصلي

Fatou Type Theorems

نام عام مواد

[Book]

ساير اطلاعات عنواني

Maximal Functions and Approach Regions /

نام نخستين پديدآور

by Fausto Biase.

محل نشرو پخش و غیره

Boston, MA :

نام ناشر، پخش کننده و غيره

Birkhäuser Boston,

تاریخ نشرو بخش و غیره

1998.

عنوان فروست

Progress in Mathematics ;

مشخصه جلد

147

متن يادداشت

I Background -- 1 Prelude -- 2 Preliminary Results -- 3 The Geometric Contexts -- II Exotic Approach Regions -- 4 Approach Regions for Trees -- 5 Embedded Trees -- 6 Applications -- Notes -- List of Figures -- Guide to Notation.

بدون عنوان

0

متن يادداشت

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.

شماره استاندارد بين المللي کتاب و موسيقي

9781461274964

عنوان

Springer eBooks

موضوع مستند نشده

Differential equations, Partial.

موضوع مستند نشده

Functions of complex variables.

موضوع مستند نشده

Global analysis (Mathematics).

موضوع مستند نشده

Mathematics.

مستند نام اشخاص تاييد نشده

Biase, Fausto.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190301081900.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y