Methods of spectral analysis in mathematical physics : by OTAMP (2006, Lund)

By OTAMP (2006, Lund)

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J. Statist. , 46(5-6):911–918, 1987. [100] F. Sobieczky. An interlacing technique for spectra of random walks and its application to finite percolation clusters. org/math/0504518. [101] P. Stollmann. Caught by disorder: A Course on Bound States in Random Media, volume 20 of Progress in Mathematical Physics. Birkh¨ auser, 2001. A. Shubin. Almost periodic functions and partial differential operators. Uspehi Mat. Nauk, 33(2(200)):3–47, 247, 1978. A. Shubin. Spectral theory and the index of elliptic operators with almostperiodic coefficients.

37] F. Germinet and A. Klein. Explicit finite volume criteria for localization in continuous random media and applications. Geom. Funct. , 13(6):1201–1238, 2003. gz. [38] F. Germinet and A. Klein. A characterization of the Anderson metal-insulator transport transition. Duke Math. , 124(2):309–350, 2004. pdf. I. Grigorchuk, P. Linnell, T. Schick, and A. Zuk. On a question of Atiyah. R. Acad. Sci. Paris S´ er. , 331(9):663–668, 2000. I. Grigorchuk and A. Zuk. The lamplighter group as a group generated by a 2-state automaton, and its spectrum.

0, 0). Hence, employing ∞ ϕ′n;j (0)ϕ′n;k (0) n=1 (λn − λ)m+1 provided m ≥ 2. , the Dirichlet eigenvalues and the Neumann data of the Dirichlet eigenfunc˜ (m) . tions. Therefore the exact same expression is obtained for Λ j,k ˜ tends to zero. 2. As λ tends to negative infinity Λ − Λ Proof. 1 the quantities Λj,k = −ψj′ (k, λ, 0) are exponentially small √ except for j = k in√which case we have Λk,k = ψk′ (k, λ, 0) = − −λ + o(1). But ˜ k,k = o(1). ˜ k,k = − −λ + o(1), we have that (Λ − Λ) since also Λ On Inverse Problems for Finite Trees 45 7.

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