On the operator norm of non-commutative polynomials in deterministic matrices and iid Haar unitary matrices
Sign Up to like & getrecommendations! Published in 2022 at "Probability Theory and Related Fields"
DOI: 10.1007/s00440-021-01101-0
Abstract: Let $U^N = (U_1^N,\dots, U^N_p)$ be a d-tuple of $N\times N$ independent Haar unitary matrices and $Z^{NM}$ be any family of deterministic matrices in $\mathbb{M}_N(\mathbb{C})\otimes \mathbb{M}_M(\mathbb{C})$. Let $P$ be a self-adjoint non-commutative polynomial. In 1998,… read more here.
Keywords: haar unitary; unitary matrices; almost surely; deterministic matrices ... See more keywords
Operator-Norm Convergence Estimates for Elliptic Homogenization Problems on Periodic Singular Structures
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-018-3887-9
Abstract: For an arbitrary periodic Borel measure μ we prove order O(ε) operator-norm resolvent estimates for the solutions to scalar elliptic problems in L2(ℝd, dμε) with ε-periodic coefficients, ε > 0. Here, με is the measure… read more here.
Keywords: estimates elliptic; norm convergence; convergence estimates; measure ... See more keywords