Non-Tangential Limits of Bloch Functions

2007 ◽  
Vol 8 (1) ◽  
pp. 277-284
Author(s):  
Daniel Girela
Keyword(s):  
Bloch Functions ◽  
Tangential Limits

Angular and Tangential Limits of Blaschke Products and their Successive Derivatives

1962 ◽  
Vol 14 ◽  
pp. 334-348 ◽  
Author(s):  
G. T. Cargo
Keyword(s):  
Blaschke Product ◽  
Common Knowledge ◽  
Holomorphic Functions ◽  
Blaschke Products ◽  
Radial Limit ◽  
Radial Limits ◽  
Almost Everywhere ◽  
Image Position ◽  
Bounded Holomorphic ◽  
Tangential Limits

In this paper, we shall be concerned with bounded, holomorphic functions of the formwhere(1)(2)and(3)B(z{an}) is called a Blaschke product, and any sequence {an} which satisfies (2) and (3) is called a Blaschke sequence. For a general discussion of the properties of Blaschke products, see (18, pp. 271-285) or (14, pp. 49-52).According to a theorem due to Riesz (15), a Blaschke product has radial limits of modulus one almost everywhere on C = {z: |z| = 1}. Moreover, it is common knowledge that, if a Blaschke product has a radial limit at a point, then it also has an angular limit at the point (see 14, p. 19 and 6, p. 457).

scholarly journals Boundary values of analytic functions without distributional point values

2004 ◽  
Vol 35 (1) ◽  
pp. 53-60 ◽  
Author(s):  
Ricardo Estrada
Keyword(s):  
Analytic Functions ◽  
Boundary Values ◽  
Tangential Limits

We give a method to construct distributions that are boundary values of analytic functions which have non-tangential limits at points where the distributional point value does not exist.

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