Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Về việc gắn liền với . | I. OPERATOR THEORY 4 1980 55-91 Copyright by INCREST 1980 ON INTERTWINING DILATIONS. VIII GR. ARSENE ZOIA CEAU ESCU c. FOIA 0. INTRODUCTION Since the existence of contractive intertwining dilations was proved in early 1968 25 it became clear that the problem of describing all of them is or will be involved in several important topics of Operator Theory and other parts of Analysis 13 . Many basic ideas concerning special cases of this problem appeared explicitely or implicitely in quite a few papers for example 1 2 3 4 5 12 21 26 and so on . There are now at hand some general descriptions of the set of all contractive intertwining dilations see 10 11 among these we quote here the following A the labelling using choice sequences see 10 or the next section which deals with the free part of the problem and B the idea of Lemma from 10 where the general problem is reduced to a very simple case. These facts are given more or less implicitely in 10 it is the aim of this paper to make explicite these labellings and the connections between them. We will heavily use the account given in 6 for the choice sequence labelling. This paper has two main results A an algorithm which connects a contractive intertwining dilation with its choice sequence Theorem below this algorithm gives more workable algorithm in seismic exploration used in Geophisics. B an explicit formula for the connection B Theorem below . This formula turns out to be a generalization of both classical and operational extrapolation formulas 1 2 3 8 9 17 18 19 22 or for example 16 Ch. IV Th. and Ch. V 4 and the characteristic function of a contraction 24 Ch. VI . Different consequences of these results for Operator Theory Differential Equations and Geophysics as well as further developments connecting explicitely our results to 3 7 14 15 16 26 27 will be given elsewhere. 56 GR. ARSENE ZOIA CEAUSESCU c. FOIA Ỷ The results of this paper had been circulated as INCREST Preprints no. 28 1978 and 76 1979.
