The theory of summability has many uses throughout analysis and applied mathematics. Engineers and physicists working with Fourier series or analytic continuation will also find the concepts of ...

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In this chapter, the matrix transformations in sequence spaces are studied and the characterizations of the classes of Schur, Kojima and Toeplitz matrices together with their versions for the series-to-sequence, sequence-to-series and series-to-series matrix transformations are given.

Matrix transformations between sequence spaces, ordinary, absolute and strong summability, KOjima-Schur theorem, Silverman-Toeplitz theorem, Schur's theorem, algebra, normed and Banach algebra, characteristic of a matrix, sequence-to-sequence, series-to-sequence, series-to-series and sequence-to-series matrix transformations, dual summability methods, arithmetics, Cesàro, Euler, Riesz and Nörlund means, Taylor, Ar, Hausdor, Borel and Abel matrices.