Typical absolute continuity for classes of dynamically defined measures
Sign Up to like & getrecommendations! Published in 2022 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2022.108258
Abstract: We consider one-parameter families of smooth uniformly contractive iterated function systems {f j } on the real line. Given a family of parameter dependent measures {μλ} on the symbolic space, we study geometric and dimensional… read more here.
Keywords: parameter; measure; typical absolute; continuity classes ... See more keywords
Absolute continuity of spectral shift
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2018.05.011
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… read more here.
Keywords: absolute continuity; continuity; spectral shift; continuity spectral ... See more keywords
Absolute continuity of distributions of polynomials on spaces with log-concave measures
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Notes"
DOI: 10.1134/s0001434617010035
Abstract: In the paper, it is proved that the distribution of a measurable polynomial on an infinite-dimensional space with log-concave measure is absolutely continuous if the polynomial is not equal to a constant almost everywhere. A… read more here.
Keywords: continuity distributions; polynomials spaces; measure; distributions polynomials ... See more keywords
Eigenvalues, absolute continuity and localizations for periodic unitary transition operators
Sign Up to like & getrecommendations! Published in 2019 at "Infinite Dimensional Analysis, Quantum Probability and Related Topics"
DOI: 10.1142/s0219025719500115
Abstract: The localization phenomenon for periodic unitary transition operators on a Hilbert space consisting of square summable functions on an integer lattice with values in a finite-dimensional Hilbert space, which is a generalization of the discrete-time… read more here.
Keywords: absolute continuity; unitary transition; transition operators; periodic unitary ... See more keywords