An extension of Lewis's Lemma, renormalization of harmonic and analytic functions, and normal families

2009 ◽  
Vol 282 (4) ◽  
pp. 540-551 ◽  
Author(s):  
Jürgen Grahl ◽  
Oliver Roth
Keyword(s):  
Analytic Functions ◽  
Normal Families ◽  
Harmonic And Analytic Functions

scholarly journals Distributional boundary values of harmonic and analytic functions

1982 ◽  
Vol 89 (1) ◽  
pp. 262-289 ◽  
Author(s):  
R Estrada ◽  
R.P Kanwal
Keyword(s):  
Analytic Functions ◽  
Boundary Values ◽  
Harmonic And Analytic Functions

Embedding theorems for weighted classes of harmonic and analytic functions

1978 ◽  
Vol 9 (2) ◽  
pp. 228-243 ◽  
Author(s):  
V. L. Oleinik
Keyword(s):  
Analytic Functions ◽  
Embedding Theorems ◽  
Harmonic And Analytic Functions

scholarly journals On Level Curves of Harmonic and Analytic Functions on Riemann Surfaces

1969 ◽  
Vol 34 ◽  
pp. 77-87
Author(s):  
Shinji Yamashitad
Keyword(s):  
Riemann Surface ◽  
Subharmonic Function ◽  
Analytic Functions ◽  
Harmonic Functions ◽  
Riemann Surfaces ◽  
Vector Lattice ◽  
Level Curves ◽  
Harmonic Majorant ◽  
Harmonic And Analytic Functions ◽  
Hyperbolic Riemann Surface

In this note we shall denote by R a hyperbolic Riemann surface. Let HP′(R) be the totality of harmonic functions u on R such that every subharmonic function | u | has a harmonic majorant on R. The class HP′(R) forms a vector lattice under the lattice operations:

Embedding theorems for weighted classes of harmonic and analytic functions

1974 ◽  
Vol 2 (2) ◽  
pp. 135-142 ◽  
Author(s):  
V. L. Oleinik ◽  
B. S. Pavlov
Keyword(s):  
Analytic Functions ◽  
Embedding Theorems ◽  
Harmonic And Analytic Functions

scholarly journals Regularization of distributions

1998 ◽  
Vol 21 (4) ◽  
pp. 625-636 ◽  
Author(s):  
Ricardo Estrada
Keyword(s):  
Analytic Functions ◽  
Sufficient Condition ◽  
Boundary Values ◽  
Necessary And Sufficient Condition ◽  
Several Variables ◽  
Necessary And Sufficient ◽  
Harmonic And Analytic Functions ◽  
Regularization Of Distributions

We give a simple necessary and sufficient condition for the existence of distributional regularizations. Our results apply to functions and distributions defined in the complement of a point, in one or several variables. We also consider functions defined in the complement of a hypersurface. We apply these results to the existence of distributional boundary values of harmonic and analytic functions.

Harmonic and analytic functions on graphs

2003 ◽  
Vol 76 (1-2) ◽  
pp. 3-15 ◽  
Author(s):  
Itai Benjamini ◽  
L�szl� Lov�sz
Keyword(s):  
Analytic Functions ◽  
Harmonic And Analytic Functions

Boundary vs. interior conditions associated with weighted composition operators

2014 ◽  
Vol 12 (5) ◽  
Author(s):  
Kei Izuchi ◽  
Yuko Izuchi ◽  
Shûichi Ohno
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Weight Functions ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Weighted Composition ◽  
The Difference ◽  
Harmonic And Analytic Functions

AbstractAssociated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk $$\mathbb{D}$$, we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior $$\mathbb{D}$$ and on the boundary $$\partial \mathbb{D}$$ respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators.

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