1. 1. Definition of Lforms. In the years 19071911 O. Toeplitz [21, 22, 23, 24]* studied a class of quadratic forms whose matrix is of the follO"ing type: (Ll) C2 C_I Co CnI CnI The elements Cn are given complex constants. Toeplitz designated these forms as Lforms and investigated in detail their relation to the analytic function defined in a neighborhood of the unit circle by the Laurent series 2 C z", n = n  00, ..., 00 this series is assumed to be convergent in a certain circular ring rl < I z I < r2, rl < 1 < r2. It is obvious that these matrices are connected with the infinite cyclic group, just as the finite cyclic matrix CO CI C2 C Co CI n r (1. 2) CnI C Co n L. c, c, Co is associated with the finite cyclic group. The main result of Toeplitz is that the spectrum of the Lform is identical with the complex values the Laurent series assumes on the unit circle I z I = 1. 1. 2. Hermitian forms. The case C = en is of particular importance the n matrix (1. 1) is in this case a Hermitian one and the associated Laurent series i8 represents a real function f(8) on the unit circle z = e , 'II" ~ 8 < '11".
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Author  :  G. P. Szego 
Publisher  :  SpringerVerlag New York Inc. 
Data Published  :  12 October 2011 
ISBN  :  1461257875 
EAN  :  9781461257875 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  880 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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