Definition
A sequence of points inside the unit disk is said to satisfy the Blaschke condition when
Given a sequence obeying the Blaschke condition, the Blaschke product is defined as
with factors
provided a ≠ 0. Here a* is the complex conjugate of a. When a = 0 take B(0,z) = z.
The Blaschke product B(z) defines a function analytic in the open unit disc, and zero exactly at the an (with multiplicity counted): furthermore it is in the Hardy class .
The sequence of an satisfying the convergence criterion above is sometimes called a Blaschke sequence.
Read more about this topic: Blaschke Product
Famous quotes containing the word definition:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)