By Hari Bercovici (auth.), T. Furuta, I. Gohberg, T. Nakazi (eds.)
This quantity is devoted to Tsuyoshi Ando, a premiere specialist in operator concept, matrix idea, advanced research, and their functions, at the celebration of his sixtieth birthday. The e-book opens along with his biography and checklist of courses. It encompasses a collection of papers protecting a extensive spectrum of subject matters starting from summary operator thought to varied concrete difficulties and purposes. the vast majority of the papers take care of issues in smooth operator concept and its functions. This quantity additionally includes papers on interpolation and final touch difficulties, factorization difficulties and difficulties attached with advanced research. The e-book will entice a large viewers of natural and utilized mathematicians.
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Extra info for Contributions to Operator Theory and its Applications: The Tsuyoshi Ando Anniversary Volume
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Al + B1D11C1)-1 BIDll = D2Dll - D 2D 1 1C 1(S! - Al + B1D11Ct}-1 BIDll +C2(s! - A1)-1[S! - Al + B1D11C1 - B1D11C1](S! - Al = D2Dll + (C2 - D 2D 1 1C 1)(s! ) + B1D11Ct}-1 BIDll + B1D11C1)-1 BIDll. o The following proposition gives a method to obtain factorizations using polynomial matrices. It establishes the existence of a factorization G = N M-l such that the McMillan degree of ( ~ ) equals the McMillan degree of G. A key step in the proof of this proposition is the following result that follows from the realization theory via polynomial models.
Changing our focus to the study of matrix rational functions, we use left and right matrix fractions of the form G = N D- 1 = D- 1 N with N, N, D, D polynomial matrices. Such factorizations are called right and left coprime factorizations respectively if there exist polynomial matrix solution to the Bezout equations XN+YD=I and respectively. A. Fuhrmann and R. Ober These polynomial coprime factorizations played an extremely important role in the development of algebraic system theory, and in particular in realization theory.
7) with {p(z), q(z)} EN! 5). 6) if and only if the Nevanlinna pair {p(z),q(z)} belongs to 8!. 11). Proof of Step 1 Since the matrix r is diagonal then Qr = QrQoQ. 15) we obtain the identity QfQ'QKQ' - QKQ'QfQ' = -iQMJM·Q·. 9) and parameters {p(z), q(z)} EN:;. 8). 18) ) = O. 8) we obtain f(z)M8(z) = {Kf(z)·Q·(QKQ·)-lQM + f(z)(I - KQ·(QKQ·)-lQ)M} (~ ~). rKf(z)(I - KQ·(QKQ·)-lQ)M (~ ~) ( :~:~ ) == O. rKM ( F 0) ( I p(z) ) _ q(z) = o. 23) p(z) == O. rK{«( ~) ( :~;~ ) ~) = - (KI' - Kr*)Q;(QI'KI'Q;)-lQI' ( = PK•rK {(1 - KI'Q;(QI'KI'Q;)-lQI') ( = PK•rK ( ~) ~ ))p(z) - ~ )) - ( ~ ) q(z)} = ( ~ ) q(z)} = q(z) == O.