3.6 Notes

Section 3.1 Introductory textbooks on harmonic analysis are Katznelson [198] and Deitmar [89]. For signal processing aspects of harmonic analysis see Oppenheim et al. [307]. Generalizations of the Parseval identity are discussed in Montgomery [275]. For inequalities see Beckenbach and Bellman [22]. The Bernstein inequality and other polynomial inequalities are treated in P lya and Szeg [331], Borwein and Erd lyi [38], and references therein. The theory of Chebyshev polynomials can be found in Szeg [392] and Mason [258].

Section 3.2 Standard texts on probability are Feller [110] and Papoulis and Pillai [313]. Although the theory of stochastic processes will be used in what follows, I have omitted introduction to it since it can be found in standard engineering textbooks, e.g. Proakis [335], Proakis and Salehi [336], and Wong and Hajek [432]. A mathematical theory of stochastic processes is presented, e.g., in Papoulis and Pillai [313] and Ross [345].

Section 3.3 A general introduction to algebraic structures can be found in Dummit and Foote [98] and Anderson [4]. For the theory of finite fields, see McEliece [263] and Lidl and Niederreiter [242]. Exponential sums over finite fields are considered in Schmidt [358]. Galois rings are treated in Wan [424]. Exponential sums over rings were considered by Kumar et al. [224], Helleseth et al. [156], and Ling and Ozbudak [245].

Section 3.4 For the theory of error correcting codes see MacWilliams and Sloane [257], van Lint [247], and Huffman and...