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Gabor Szegoe : Collected Papers: 1945-1972. Softcover reprint of the original 1st ed. 1982.
・ISBN 978-1-4612-5787-5 paper EUR 49.99
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| 著者・編者 | Szegoe, Gabor P., |
|---|---|
| シリーズ | Contemporary Mathematicians |
| 出版社 | (Springer-Verlag New York Inc., US) |
| 出版年月 | 2011 |
| ページ数 | 880 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-22243＞ |
解説
1. 1. Definition of L-forms. In the years 1907-1911 O. Toeplitz [21, 22, 23, 24]* studied a class of quadratic forms whose matrix is of the follO\\"ing type: (Ll) C-2 C_I Co C-n-I Cn-I The elements Cn are given complex constants. Toeplitz designated these forms as L-forms 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) Cn-I 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 L-form 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".