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Absolutely continuous spectrum of fourth order difference operators with unbounded coefficients on a Hilbert space

Master's Thesis 2015 54 Pages

Mathematics - Analysis

Summary

In this study, the author has investigated the absolutely continuous spectrum of a fourth order self-adjoint extension operator of minimal operator generated by difference equation defined on a weighted Hilbert space with the weight function w(t) > 0, t ∈ N where p(t), q(t), r(t) and m(t) are real-valued functions.

The author has applied the M-matrix theory as developed in Hinton and Shaw in order to compute the spectral multiplicity and the location of the absolutely continuous spectrum of self-adjoint extension operator. These results have been an extension of some known spectral results of fourth order differential operators to difference setting. Similarly, they have extended results found in Jacobi matrices.

In this thesis, chapter 1 is about introduction and some preliminary results including literature review, objectives, methodology and basic definitions. In chapter 2, the author has given the results on the computation of the eigenvalues, dichotomy conditions and some results on singular continuous spectrum. Chapter 3 contains the main results in deficiency indices, absolutely continuous spectrum and the spectral multiplicity. Finally, the author has summarized his results in chapter 4 and also highlighted areas of further research.

Details

Pages
54
Year
2015
ISBN (eBook)
9783668531505
ISBN (Book)
9783668531512
File size
583 KB
Language
English
Catalog Number
v375444
Grade
A
Tags
Hilbert spaces M-matrix self-adjoint operators spectrum eigenvalues difference operators sturm Liovile operators

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Title: Absolutely continuous spectrum of fourth order difference operators with unbounded coefficients on a Hilbert space