Analytic Functions of Several Complex Variables by Robert C. Gunning, Hugo Rossi

By Robert C. Gunning, Hugo Rossi

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3. 5) hold. 5) as F but with Ci replaced by diag[ci,1 , . . , ci,N ] for F0 and by ⎤ ⎡ 0 0 0 ... 0 0 ⎢ (ci )2,1 0 0 ... 0 0⎥ ⎥ ⎢ ⎢ (ci )3,1 (ci )3,2 0 ... 6) Ci = ⎢ .. ⎥ .. .. ⎢ . ⎥ . . ⎥ ⎢ ⎣(ci )N −1,1 (ci )N −1,2 (ci )N −1,3 . . 0 0⎦ (ci )N,1 (ci )N,2 (ci )N,3 . . (ci )N,N −1 0 for F . Then GF = G + K, where G is an abbreviated notation for GF0 and K= 0N F 0N . 7) where for s = 1, 2, . . 30) (once again, with Ci replaced by ci,s for i = ±1, ±2), where c−2,s c−1,s c1,s Y0 = − , Y−1 = − + , Y−1 = 1.

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