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Perturbations of selfadjoint operators with discrete spectrum

Adduci, James
http://rave.ohiolink.edu/etdc/view?acc_num=osu1313520875

Abstract Details

2011, Doctor of Philosophy, Ohio State University, Mathematics.
Consider a selfadjoint operator A whose spectrum is a set of eigenvalues {t_1 < t_2 < ....} with corresponding eigenvectors {f_1, f_2,...}. Now introduce a perturbation B and set L = A+B. We prove that if t_{n+1} - t_n > C n^{a-1} and lim || Bf_n ||n^{1-a} = 0 for some fixed a > 1/2 then the spectrum of L = A + B is discrete, eventually simple and the set of eigenvectors of L = A + B plus at most finitely many associated vectors form an unconditional basis. As an application we consider Schrodinger operators of the form Ly = -y'' + |x|^c y + b(x)y on L^2(R) where b is a possible complex-valued function and c > 1.
Boris Mityagin (Advisor)
45 p.
Mathematics
Unconditional basis; discrete Hilbert transform

Recommended Citations

Citations

  • Adduci, J. (2011). Perturbations of selfadjoint operators with discrete spectrum [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1313520875

    APA Style (7th edition)

  • Adduci, James. Perturbations of selfadjoint operators with discrete spectrum. 2011. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1313520875.

    MLA Style (8th edition)

  • Adduci, James. "Perturbations of selfadjoint operators with discrete spectrum." Doctoral dissertation, Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1313520875

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.