## Walsh Series, An Introduction to Dyadic Harmonic AnalysisThis book provides a broadly based, theoretical monograph on the Walsh System, a system that is the simplest non-trivial model for harmonic analysis and shares many properties with the trigonometric system. It gives a thorough introduction to foundations of Walsh-Fourier analysis introducing the main techniques and fundamental problems in a way that makes the literature accessible. It also shows how the theory of Walsh-Fourier analysis relates to other aspects of harmonic analysis. The book will be of interest to postgraduate students in pure and applied mathematics, and those studying numerical analysis and computational mathematics. |

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abelian group absolute constant analogue Banach space belongs binary coefficients Borel measure choose classical compact conclude Consequently converges a.e. Corollary countable defined definition Dirichlet kernels dyadic group dyadic intervals dyadically differentiable equivalent estimate exists following result Fourier series Franklin system function g G L1 Haar measure Haar system Hadamard transform Hardy spaces Hence holds hypothesis implies inequality integer isomorphism L1 norm Lebesgue Lebesgue measure limsup martingale measure preserving modulus of continuity monotone Moreover non-negative Notice observe obtain operator orthogonal orthonormal system partial sums particular product system proof of Theorem prove quasi-measure real numbers Riesz-Fischer theorem satisfies Schipp sequence subset suffices to show Suppose Theorem 12 Theorem 9 trigonometric U-set uniformly bounded verify Vilenkin systems Walsh functions Walsh polynomial Walsh series Walsh system Walsh-Fourier coefficients Walsh-Fourier series Walsh-Fourier transform weak type