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Absolute Continuity
The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform
Boris Solomyak – One of the best experts on this subject based on the ideXlab platform.
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Absolute Continuity of non homogeneous self similar measures
Advances in Mathematics, 2018Co-Authors: Santiago Saglietti, Pablo Shmerkin, Boris SolomyakAbstract: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.
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Absolute Continuity of spectral shift
Journal of Functional Analysis, 2019Co-Authors: Mark Malamud, Hagen Neidhardt, Vladimir PellerAbstract: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.
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Absolute Continuity of spectral shift
arXiv: Functional Analysis, 2018Co-Authors: Mark Malamud, Hagen Neidhardt, Vladimir PellerAbstract: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.
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The Vitali integral convergence theorem and uniform Absolute Continuity
Canadian Journal of Mathematics, 1991Co-Authors: Elizabeth M. Bator, Russell G. Bilyeu, Paul W. LewisAbstract: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.