DENSITY OF MARKOV SYSTEMS AND ZEROS OF CHEBYSHEV POLYNOMIALS

(整期优先)网络出版时间:1998-02-12
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Weraiseandpartlyanswerthequestion:whetherthereexistsaMarkovsystemwithrespecttowhichthezerosoftheChebyshevpolynomialsaredense,butthemaximumlengthofazerofreeintervalofthenthChebyshevpolynomialdoesnottendstozero.Wealsodrawtheconclu-tionthataMarkovsystem,underanadditionalassumption,isdenseifandonlyifthemaxi-mumlengthofazerofreeintervalofthenthassociatedChebyshevpolynomialtendstozero.