The Phragmen-Lindelof Principle, first formulated by Lars Edvard Phragmen and Ernst Leonard Lindelof in 1908, is a technique in complex analysis that uses an auxiliary parameterized function to prove that a holomorphic function is bounded on an unbounded domain, given some usually mild condition constraining how fast the function's size can grow on that domain. It generalizes the maximum modulus principle, which by itself applies only to bounded domains.
Facts
StatementA technique employing an auxiliary, parameterized function to prove that a holomorphic function is bounded on an unbounded domain, given a usually mild condition constraining the growth of |f| on that domain; it generalizes the maximum modulus principle, which applies only to bounded domains. 1 Classification
Statement FormCharacterization Theorem 1 Sources
1. Phragmen-Lindelof principle (Wikipedia)
Introduction, description of the method
a technique which employs an auxiliary, parameterized function to prove the boundedness of a holomorphic function
Introduction, first sentence
first formulated by Lars Edvard Phragmén (1863-1937) and Ernst Leonard Lindelöf (1870-1946) in 1908
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