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    STUDIA MATHEMATICA - Issue no. 3 / 2009  
         
  Article:   THE CHARACTERS OF THE BLASCHKE-GROUP OF THE ARITHMETIC FIELD.

Authors:  ILONA SIMON. 		 
       
         
  Abstract:  We consider a locally compact metric space, B with arithmetic addition and multiplication, which is closely related to the usual multiplication of real numbers in the dyadic system. This results a non-Archimedian local field, the so-called 2-adic local field. Some orthogonal series are studied with respect the inner product defined with the Haar-measure μ. The Blaschke-functions defined on the 2-adic field,

form a commutative group with respect to the function composition, the so-called Blaschke-group. We shall determine the characters of this group. By  means of the exponential and tangent functions on the 2-adic field and the  characters of its additive group we can identify the desired characters. We  consider Fourier-series with respect to these characters and summability questions are examined. A simple recursion leads to the FFT-algorithm, the so-called Fast-Fourier Transform.


Key words and phrases. p-adic theory, local fields, character groups, (C,1)-summability, Fast-Fourier Transform. 		 
         
     
         
         
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