Phragmén–Lindelöf principle

In complex analysis, the Phragmén–Lindelöf principle (or method), first formulated by Lars Edvard Phragmén (1863–1937) and Ernst Leonard Lindelöf (1870–1946) in 1908, is a technique which employs an auxiliary, parameterized function to prove the boundedness of a holomorphic function f {\displaystyle f} (i.e., | f ( z ) | < M ( z ∈ Ω ) {\displaystyle |f(z)|<M\ \ (z\in \Omega )} ) on an unbounded domain Ω {\displaystyle \Omega } when an additional (usually mild) condition constraining the growth of | f | {\displaystyle |f|} on Ω {\displaystyle \Omega } is given. It is a generalization of the maximum modulus principle, which is only applicable to bounded domains.

Source: Wikipedia — Phragmén–Lindelöf principle (CC BY-SA 4.0)

Phragmén–Lindelöf principle

In complex analysis, the Phragmén–Lindelöf principle (or method), first formulated by Lars Edvard Phragmén (1863–1937) and Ernst Leonard Lindelöf (1870–1946) in 1908, is a technique which employs an auxiliary, parameterized function to prove the boundedness of a holomorphic function f {\displaystyle f} (i.e., | f ( z ) | < M ( z ∈ Ω ) {\displaystyle |f(z)|<M\ \ (z\in \Omega )} ) on an unbounded domain Ω {\displaystyle \Omega } when an additional (usually mild) condition constraining the growth of | f | {\displaystyle |f|} on Ω {\displaystyle \Omega } is given. It is a generalization of the maximum modulus principle, which is only applicable to bounded domains.

Source: Wikipedia "Phragmén–Lindelöf principle" · CC BY-SA 4.0

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