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.
Yuhu Feng - One of the best experts on this subject based on the ideXlab platform.
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A note on indefinite integrals and Absolute Continuity for fuzzy-valued mappings
Fuzzy Sets and Systems, 2004Co-Authors: Yuhu FengAbstract:Abstract This note is to define the Absolute Continuity for fuzzy-valued mappings and to give the necessary and sufficient conditions for the Newton–Leibniz formula to hold.
Santiago Saglietti - 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.