Simultaneous smoothing and interpolation with respect to E. Borel's Theorem

1993 ◽  
Vol 61 (2) ◽  
pp. 150-159 ◽  
Author(s):  
Markus Poppenberg
Keyword(s):  
Borel’S Theorem

scholarly journals Borel's theorem for generalized functions

1985 ◽  
Vol 81 (2) ◽  
pp. 179-183 ◽  
Author(s):  
H. Biagioni ◽  
J. Columbeau
Keyword(s):  
Generalized Functions ◽  
Borel’S Theorem

The Algebraic Independence of Certain Exponential Functions

1976 ◽  
Vol 28 (5) ◽  
pp. 968-976
Author(s):  
W. Dale Brownawell
Keyword(s):  
Meromorphic Functions ◽  
Entire Functions ◽  
General Theorem ◽  
Algebraic Independence ◽  
Exponential Functions ◽  
Linearly Independent ◽  
Borel’S Theorem ◽  
Picard’S Theorem ◽  
Picard's Theorem ◽  
Special Case

In 1897 E. Borel proved a general theorem which implied as a special case the following result equivalent to his celebrated generalization of Picard's theorem [2]: If f1 … ,fm are entire functions such that for each, C then the functions exp f1, … , exp f/m are linearly independent over C. In 1929 R. Nevanlinna [6] extended Borel's theorem to consider arbitrary C-linearly independent meromorphic functions < ϕi, … , < ϕm satisfying < ϕ1 + … + ϕm = 1.

scholarly journals A generalization of Borel's theorem and microlocal Gevrey regularity in involutive structures

2008 ◽  
Vol 245 (10) ◽  
pp. 2846-2870 ◽  
Author(s):  
Z. Adwan ◽  
G. Hoepfner
Keyword(s):  
Gevrey Regularity ◽  
Borel’S Theorem

scholarly journals Word maps on perfect algebraic groups

2018 ◽  
Vol 28 (08) ◽  
pp. 1487-1515 ◽  
Author(s):  
Nikolai Gordeev ◽  
Boris Kunyavskiĭ ◽  
Eugene Plotkin
Keyword(s):  
Algebraic Groups ◽  
New Ideas ◽  
Borel’S Theorem ◽  
Semisimple Algebraic Groups

We extend Borel’s theorem on the dominance of word maps from semisimple algebraic groups to some perfect groups. In another direction, we generalize Borel’s theorem to some words with constants. We also consider the surjectivity problem for particular words and groups, give a brief survey of recent results, present some generalizations and variations and discuss various approaches, with emphasis on new ideas, constructions and connections.

A strengthening of Borel's theorem and its application

1990 ◽  
Vol 48 (2) ◽  
pp. 231-234
Author(s):  
M. N. Sheremeta
Keyword(s):  
Borel’S Theorem

Borel's theorem ona-points and exceptional values of Entire and Meromorphic Functions

1953 ◽  
Vol 59 (1) ◽  
pp. 88-93 ◽  
Author(s):  
S. M. Shah ◽  
S. K. Singh
Keyword(s):  
Meromorphic Functions ◽  
Borel’S Theorem

A Concise Proof of Borel's Theorem on Coefficient Bounds

1967 ◽  
Vol 74 (9) ◽  
pp. 1094
Author(s):  
R. A. Whiteman
Keyword(s):  
Coefficient Bounds ◽  
Borel’S Theorem

scholarly journals Deformation quantization and Borel's theorem in locally convex spaces

2007 ◽  
Vol 180 (1) ◽  
pp. 77-93
Author(s):  
Miroslav Engliš ◽  
Jari Taskinen
Keyword(s):  
Deformation Quantization ◽  
Locally Convex Spaces ◽  
Borel’S Theorem ◽  
Locally Convex ◽  
Convex Spaces

On E. Borel's theorem

1988 ◽  
Vol 282 (2) ◽  
pp. 299-313 ◽  
Author(s):  
Hans-Joachim Petzsche
Keyword(s):  
Borel’S Theorem

Peano’s Unnoticed Proof of Borel’s Theorem

2014 ◽  
Vol 121 (1) ◽  
pp. 69
Author(s):  
Ádám Besenyei
Keyword(s):  
Borel’S Theorem
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