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Additional resources for Functional Analysis II
It is the characteristic function of the ~, _ unitary colligation (N,~(S -~), v(S*-~);C~(S(~)), IIv(S*_~), Pv(S*-~)'0) and with - ~ , ~ e ¢~, the operator Pv(s*-~)(l - zC~(S(v)D-~ is the projection of H onto £-p v(S*-~) parallel to R(S-£); H = v ( S * - ~ ) + E ( S - ~ ) , direct sum, £6~-~. Hence it is z= clear that Y~(z) =Y (z) , or, in other words, that Y--~is the characteristic function of the isometric operator C (S). As to the boundary behaviour of Y with $ =%%_- ~ , % E ~ , a unique ~ 6 v ( S D0(Y (~)) is the set of all ~ 6 v ( S * - ~ ) -~) such that ~ - ~ 6 R ( S - % ) more, D0(Y (I)) is the set of all ~ 6~(S*-~) on ~ we note that for which there exists and then Y ( ~ ) ~ = ~ , ~ 6 D 0 ( Y ($)).
Nauk SSSR Amer. Math. Soc. Transl. (2) 40 1-37). V. ~traus, On the extensions of syrmnetric operators depending on a parameter, Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965) 1389-1416 Soc. Transl. V. ~traus, On one-parameter Amer. Math. families of extensions of a symmetric operator, Akad. Nauk SSSR Ser. Mat. 30 (1966) 1325-1352 Soc. Transl. (English translation: (2) 61 (1967) 113-141). (English translation: Izv. Amer. Math. (2) 90 (1970) 135-164). V. ~traus, On the extensions and the characteristic tor, ~zv.
Traus, On some questions University, Dissertation, in the theory of symmetric operators, Moscow State 1960. V. ~traus, Characteristic functions of linear operators, Ser. Mat. 24 (1960) 43-74 (English translation: (1964) Izv. Akad. Nauk SSSR Amer. Math. Soc. Transl. (2) 40 1-37). V. ~traus, On the extensions of syrmnetric operators depending on a parameter, Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965) 1389-1416 Soc. Transl. V. ~traus, On one-parameter Amer. Math. families of extensions of a symmetric operator, Akad.