Relations Between Hankel and Toeplitz Operatorsin Other (Other) by Dgoodz19
Your Price: $21.00 (30% discount)
You Save: $9.00
The Hankel operators whose matrices with respect to the standard basis for H have only a nite number of entries dierent from 0 can be described in very explicitly. Note that H has this property whenever e for any H2. It is also obvious that if H has this property, then ein is in H for some nonnegative integer n. The following sharpening of this statement is less obvious. Theorem . If a Hankel operator has a matrix with respect to the stan- dard basis for H that has only a finite number of entries different from 0, and if c is the norm of the operator, then there exists a finite Blaschke product B and a nonnegative integer n such that cein B is a symbol for the Hankel operator.
Proof. The theorem is trivial if the operator is 0; in all...