Comparative Analysis of Spectral Theory of Second Order Difference and Differential Operators with Unbounded Odd Coefficient
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초록
We show that selfadjoint operator extensions of minimal second order difference operators have only discrete spectrum when the odd order coefficient is unbounded but grows or decays according to specific conditions. Selfadjoint operator extensions of minimal differential operator under similar growth and decay conditions on the coefficients have a absolutely continuous spectrum of multiplicity one.
Abstract
We show that selfadjoint operator extensions of minimal second order difference operators have only discrete spectrum when the odd order coefficient is unbounded but grows or decays according to specific conditions. Selfadjoint operator extensions of minimal differential operator under similar growth and decay conditions on the coefficients have a absolutely continuous spectrum of multiplicity one.
참고문헌 (11)
- H. Behncke, "Spectral theory of higher order differential operators", Proc. London Math. Soc., 93(1), pp.139~160 (2006)
- H. Behncke, "Spectral analysis of fourth order differential operators III", Math. Nachr, 283(11), pp.1558~1574 (2010)
- H. Behncke, "Spectral theory of hamiltonian systems with almost constant coefficients", J. Differential Equations, 250, pp.1408~1426 (2011)
- H. Behncke, "Spectral theory of difference operators with almost constant coefficients", J. Difference Equ. Appl, 17(5), pp.677~695 (2011)
- H. Behncke, "Spectral theory of higher order difference operators", J. Difference Equ. Appl, 19(12), pp.1983~2028 (2013)
- D. B. Hinton, "On the Titchmarsh-Weyl coefficients for S-Hermitian systems I", Math. Nachr, 163, pp.323~342 (1993)
- C. Remling, "The absolutely continuous spectrum of one-dimensional Schr¨odinger operators", Math. Phys. Anal. Geom, 10, pp.359~373 (2007)
- C. Remling, "The absolutely continuous spectrum of Jacobi matrices", Ann. Math, 174, pp.125~171 (2011)
- P. Walker, "A vector-matrix formulation for formally symmetric ordinary differential equations with applications to solutions of integrable square", J. London Math. Soc., 9, pp.151~159 (1975)
- J. Weidmann, "Spectral theory of ordinary differential operators" (1987), Springer-Verlag
- Y. Shi, "Weyl-Titchmarsh theory for a class of discrete linear Hamiltonian systems", Linear Algebra Appl, 416, pp.452~519 (2006)