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656,771
Singular continuous spectrum is generic
 Bull. Am. Math. Soc
, 1994
"... Abstract. In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spectrum are a dense Gδ. In the spectral analysis of various operators of mathematical physics, a key step, often t ..."
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Cited by 15 (2 self)
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Abstract. In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spectrum are a dense Gδ. In the spectral analysis of various operators of mathematical physics, a key step, often
Operators With Singular Continuous Spectrum, V. Sparse Potentials
 TO APPEAR: PROC. AMER. MATH. SOC.
, 1995
"... By presenting simple theorems for the absence of positive eigenvalues for certain onedimensional Schrödinger operators, we are able to construct explicit potentials which yield purely singular continuous spectrum. ..."
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Cited by 79 (10 self)
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By presenting simple theorems for the absence of positive eigenvalues for certain onedimensional Schrödinger operators, we are able to construct explicit potentials which yield purely singular continuous spectrum.
Singular Continuous Spectrum for Palindromic Schrödinger Operators
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 1995
"... We give new examples of discrete Schrödinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potential x in X for which the operator has no eigenvalues implies th ..."
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Cited by 68 (5 self)
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We give new examples of discrete Schrödinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potential x in X for which the operator has no eigenvalues implies
Imbedded Singular Continuous Spectrum For Schrödinger Operators
 Evolutionary Algorithms in Engineering Applications
, 1997
"... We construct examples of potentials V (x) satisfying jV (x)j where the function h(x) is growing arbitrarily slowly, such that the corresponding Schrödinger operator has imbedded singular continuous spectrum. This solves one of the fifteen "twentyfirst century" problems for Schrödinger ope ..."
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Cited by 12 (3 self)
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We construct examples of potentials V (x) satisfying jV (x)j where the function h(x) is growing arbitrarily slowly, such that the corresponding Schrödinger operator has imbedded singular continuous spectrum. This solves one of the fifteen "twentyfirst century" problems for Schrödinger
Operators with singular continuous spectrum, II: Rank one operators
 J. ANAL. MATH
, 1996
"... For an operator, A, with cyclic vector ϕ, we study A + λP where P is the rank one projection onto multiples of ϕ. If [α, β] ⊂ spec(A) andA has no a.c. spectrum, we prove that A + λP has purely singular continuous spectrum on (α, β) for a dense Gδ of λ’s. ..."
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Cited by 179 (32 self)
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For an operator, A, with cyclic vector ϕ, we study A + λP where P is the rank one projection onto multiples of ϕ. If [α, β] ⊂ spec(A) andA has no a.c. spectrum, we prove that A + λP has purely singular continuous spectrum on (α, β) for a dense Gδ of λ’s.
THE SINGULAR CONTINUOUS SPECTRUM AND NONCLOSED INVARIANT SUBSPACES
, 2004
"... Dedicated to Israel Gohberg on the occasion of his 75th birthday ABSTRACT. Let A be a bounded selfadjoint operator on a separable Hilbert space H and H0 ⊂ H a closed invariant subspace of A. Assuming that H0 is of codimension 1, we study the variation of the invariant subspace H0 under bounded sel ..."
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selfadjoint perturbations V of A that are offdiagonal with respect to the decomposition H = H0 ⊕ H1. In particular, we prove the existence of a oneparameter family of dense nonclosed invariant subspaces of the operator A+V provided that this operator has a nonempty singular continuous spectrum. We
Generic Subsets in Spaces of Measures and Singular Continuous Spectrum
"... Abstract. We discuss recent results of ours showing that geometric disorder leads to some purely singularly continuous spectrum generically. This is based on a slight extension of Simons Wonderland theorem. Our approach to this theorem relies on the study of generic subsets of certain spaces of meas ..."
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Cited by 1 (1 self)
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Abstract. We discuss recent results of ours showing that geometric disorder leads to some purely singularly continuous spectrum generically. This is based on a slight extension of Simons Wonderland theorem. Our approach to this theorem relies on the study of generic subsets of certain spaces
SINGULAR CONTINUOUS SPECTRUM FOR CERTAIN QUASICRYSTAL SCHRÖDINGER OPERATORS
"... Abstract. We give a short introduction into the theory of onedimensional discrete Schrödinger operators associated to quasicrystals. We then report on recent results, obtained in jont work with D. Damanik, concerning a special class of these operators viz QuasiSturmian operators. These results sho ..."
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show, in particular, uniform singular continuous spectrum of Lebesgue measure zero. 1.
Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians
 Comm. Pure Appl. Math
, 1986
"... We consider a selfadjoint operator, A, and a selfadjoint rankone projection, P, onto a vector, 9, which is cyclic for A. In terms of the spectral measure dp;, we give necessary and sufficient conditions for A + A P to have empty singular continuous spectrum or to have only point spectrum for a.e. A ..."
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Cited by 122 (16 self)
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We consider a selfadjoint operator, A, and a selfadjoint rankone projection, P, onto a vector, 9, which is cyclic for A. In terms of the spectral measure dp;, we give necessary and sufficient conditions for A + A P to have empty singular continuous spectrum or to have only point spectrum for a
Results 1  10
of
656,771