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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

From the Preface (1955): The first part of the present exposition is devoted to the theory of Toeplitz forms. The second part deals with applications, in particular to the calculus of probability and mathematical statistics. Neither part claims completeness in any way. Our purpose has been to elucidate the principal ideas of this remarkable chapter of modern analysis and to help the interested student of mathematical statistics to acquire a working knowledge of the subject. The somewhat protracted Chapter 1 explains not only the notation employed but contains also the definition of important...

Deals with the theory of Toeplitz forms. This work also focuses on applications, in particular to the calculus of probability and mathematical statistics. It intends to elucidate the principal ideas of this chapter of modern analysis and to help the interested student of mathematical statistics to acquire a working knowledge of the subject.