✦ LIBER ✦
Toeplitz Matrices with an Exponential Growth of Entries and the First Szegö Limit Theorem
✍ Scribed by Alexander Sakhnovich
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 220 KB
- Volume
- 171
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
The Toeplitz (or block Toeplitz) matrices S(r)=[s j&k ] r k, j=1 , generated by the Taylor coefficients at zero of analytic functions .(*)= s0 2 + p=1 s & p * p and (+)= s0 2 + p=1 s p + p , are considered. A method is proposed for removing the poles of . and or, in other words, for replacing S( ), whose entries grow exponentially, by a matrix S ( )=[s^j &k ] k, j=1 with better behaviour and the same asymptotics of 2 (r)=det S (r) (r Ä ) as the sequence 2 r =det S(r). A Szego -type limit formula for the case when S(r)=S(r)* (r n 0 ) have a fixed number of negative eigenvalues is obtained.