Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1994. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 22)
BLAHOTA, I., Relation between Dirichlet kernels with respect to Vilenkin-like systems
Relation between Dirichlet kernels . . . 113 1.2. Let x-y e I t,t,j £ N, 0 < j < m t. Then x 0-y 0 = 0,..., x t~i yt-i = o, ajM t(x)â jM t(y) = HjMt)/ \ <V (zo, ni, • • •, n t1, n u n t+ ï _1 (jMt), s «1 «i, • • •, n t-i,n u n n +i ,•••)••• —t(jM t ) / \ a jM i(x)â jM t(x) = \a jM t(x)\ = 1. If x — y G /<, i, j» G N, 0 < j < m Í 5 then This complétés the proof of the first part of the theorem. s 2. Necessity. If n — Yh nkMk, then let k=0 In this case does not exist such j £ P that ctj(x) = 1. 2.1. Now we suppose that n ^ {jMh\h,j G N}. Let t be defined in the foHowing way t: = imn{k\ n<M k]k,ne N}. Let x' := (0,0,..., 0, x t := 1,0,...), t G N and y' := (0,0,0,...). In this case n — 1 W.vO = £**(«') = k=0 n— 1 n— 1 c J] = c £ - y 1) = - V), A:=0 k= 0 where c ^ 1. We prove that D%(x' — y') / 0, thus in this case D%(x' — y')?Dx(x\y'). But fc=0 V 1 7 V 1 '
