Summability Theory And Its Applications

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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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Spectrum of Some Particular Limitation Matrices

Pp. 193-230 (38)

Feyzi Basar

Abstract

In this chapter, the spectrum and the fine spectrum of the Cesàro operator C1, the difference operator (1), the generalized difference operator B(r; s) and the operator generated by the triple band matrix B(r; s; t) acting on the sequence spaces c0, c, lp and bvp with respect to Goldberg's classification are determined, where 1 ≤ p < ∞.

Keywords:

Spectrum and resolvent of an operator, fine spectrum of an operator with respect to Goldberg's classification, subdivisions of spectrum, point spectrum, continuous spectrum and residual spectrum, approximate point spectrum, defect spectrum and compression spectrum.