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Absolute Continuity

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Boris Solomyak – One of the best experts on this subject based on the ideXlab platform.

  • Absolute Continuity of non homogeneous self similar measures
    Advances in Mathematics, 2018
    Co-Authors: Santiago Saglietti, Pablo Shmerkin, Boris Solomyak
    Abstract:

    Abstract We prove that self-similar measures on the real line are Absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S.-M. Ngai and Y. Wang. While recently there has been much progress in understanding Absolute Continuity for homogeneous self-similar measures, this is the first improvement over the classical transversality method in the general (non-homogeneous) case. In the course of the proof, we establish new results on the dimension and Fourier decay of a class of random self-similar measures.

Vladimir Peller – One of the best experts on this subject based on the ideXlab platform.

  • Absolute Continuity of spectral shift
    Journal of Functional Analysis, 2019
    Co-Authors: Mark Malamud, Hagen Neidhardt, Vladimir Peller
    Abstract:

    Abstract In this paper we develop the method of double operator integrals to prove trace formulae for functions of contractions, dissipative operators, unitary operators and self-adjoint operators. To establish the Absolute Continuity of spectral shift, we use the Sz.-Nagy theorem on the Absolute Continuity of the spectral measure of the minimal unitary dilation of a completely nonunitary contraction. We also give a construction of an intermediate contraction for a pair of contractions with trace class difference.

  • Absolute Continuity of spectral shift
    arXiv: Functional Analysis, 2018
    Co-Authors: Mark Malamud, Hagen Neidhardt, Vladimir Peller
    Abstract:

    In this paper we develop the method of double operator integrals to prove trace formulae for functions of contractions, dissipative operators, unitary operators and self-adjoint operators. To establish the Absolute Continuity of spectral shift, we use the Sz.-Nagy theorem on the Absolute Continuity of the spectrum of the minimal unitary dilation of a completely nonunitary contraction. We also give a construction of an intermediate contraction for a pair of contractions with trace class difference.

Paul W. Lewis – One of the best experts on this subject based on the ideXlab platform.

  • The Vitali integral convergence theorem and uniform Absolute Continuity
    Canadian Journal of Mathematics, 1991
    Co-Authors: Elizabeth M. Bator, Russell G. Bilyeu, Paul W. Lewis
    Abstract:

    AbstractA geometric version of the Vitali integral convergence theorem is established. Parameterized versions of results on uniform Absolute Continuity in spaces of measures suggested by the convergence theorem are studied.