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Extra resources for Complex Vector Functional Equations

Sample text

K). We can write the above equalities in a general form / r ( X i , X 2 , . . , Xp, Y i , Y2,. . 19) min (q—l,fc+l—r) = 2_^ (— I ) * •Pri(Xi+i,Xi_(-2, . . ,Xp) -fri(Xi+i,Xi+2,. . , X p , X i , X 2 , • . ,Xj+p) 44 General Classes of Cyclic Functional Equations 9-1 + ( _ I)'" 2^i -^rt(Xj + i,Xj+2,- . , X p , Y j + i , Y j + 2 , . . , Yq) i—n—r+1 n—p + (_1)' 2^, i=max _ ^r»(Xi+i,Xj+2, •.. ,Xp) (q,n—r+1) p-1 + ^ ^ (""I)" ' • P ' » + r , n - i ( X i , X 2 , . . ,Xj_|_p, t=max (n—p+l,n—r+1) Xj+i, Xj+2 > • • •j Xp) n—q + 2 ^ (—1)" *-Fi+r,n-i(Xi,X2,.

Y j + , ) 2^ i=max(n—

Y,) i=n—r+1 n—p + 2__, { — 1)* i=max (q,n—r+1) -Fr«(X{+i,X;+2, • • • , X p ) p-1 + ^_, ( — 1)™ ' • F i + r , n - i ( X i , X 2 , . . , X i + p , X j + i , X i + 2 , . . , X p ) i=max (n—p+l,n—r+1) n—g + E (*"•'•)" i=max (p,n—r+1) l -^i+r,n-i(Xi,X2,. ,Xj+p) n-1 i Fi+r,n-i(X\, X 2 , . . ,Xj_|_p, Y i , Y 2 , . . , X p ) (r = k + p - n + 1,... ,k - q + 1); Paracyclic Functional Equation 43 / r ( X 1 , X 2 , . . ,Xp, Y i , Y2, . . , Yg) k—r ^ ( — I ) = 1 •PVt(Xi+i,Xi+2,... , X P , Yj+i, Y j + 2 , .