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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