ﻻ يوجد ملخص باللغة العربية
Pauli spin matrices, Pauli group, commutators, anti-commutators and the Kronecker product are studied. Applications to eigenvalue problems, exponential functions of such matrices, spin Hamilton operators, mutually unbiased bases, Fermi operators and Bose operators are provided.
We generalize to multi-commutators the usual Lieb-Robinson bounds for commutators. In the spirit of constructive QFT, this is done so as to allow the use of combinatorics of minimally connected graphs (tree expansions) in order to estimate time-depen
Hankel operators lie at the junction of analytic and real-variables. We will explore this junction, from the point of view of Haar shifts and commutators. An decomposition of the commutator [H,b] into paraproducts is presented.
Commutators and anticommutators of gamma matrices with arbitrary numbers of (antisymmetrized) indices are derived.
We establish the necessary and sufficient conditions for those symbols $b$ on the Heisenberg group $mathbb H^{n}$ for which the commutator with the Riesz transform is of Schatten class. Our main result generalises classical results of Peller, Janson-
It is shown that product BMO of Chang and Fefferman, defined on the product of Euclidean spaces can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of Coifman, Rochberg, and Weiss,