In mathematics, the maximum modulus principle in complex analysis states that if f is a holomorphic function, then the modulus cannot exhibit a true local maximum that is properly within the domain of f.
In other words, either f is a constant function, or, for any point z0 inside the domain of f there exist other points arbitrarily close to z0 at which |f | takes larger values.
Read more about Maximum Modulus Principle: Formal Statement, Sketch of The Proof, Physical Interpretation, Applications
Famous quotes containing the words maximum and/or principle:
“I had a quick grasp of the secret to sanityit had become the ability to hold the maximum of impossible combinations in ones mind.”
—Norman Mailer (b. 1923)
“The mode of founding a college is, commonly, to get up a subscription of dollars and cents, and then, following blindly the principles of a division of labor to its extreme,a principle which should never be followed but with circumspection,to call in a contractor who makes this a subject of speculation,... and for these oversights successive generations have to pay.”
—Henry David Thoreau (18171862)