Results 41 to 50 of about 736 (56)
Strong continuity on Hardy spaces [PDF]
arXiv, 2016 We prove the strong continuity of spectral multiplier operators associated with dilations of certain functions on the general Hardy space $H^1_L$ introduced by Hofmann, Lu, Mitrea, Mitrea, Yan. Our results include the heat and Poisson semigroups as well as the group of imaginary powers.
arxiv
On multidimensional Bochner-Phillips functional calculus [PDF]
arXiv, 2019 The functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the condition for holomorphy of semigroups, generated by operators which arisen in the calculus is given, and in the one-dimensional case the moment inequality for such operators is proved.
arxiv
On the Ehrenfest theorem of quantum mechanics [PDF]
, 2009 We give a mathematically rigorous derivation of Ehrenfest's equations for the evolution of position and momentum expectation values, under general and natural assumptions which include atomic and molecular Hamiltonians with Coulomb interactions.
arxiv +1 more source
The unbounded extension of Hille-Phillips functional calculus [PDF]
arXiv, 2019 The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is given. Connections of this calculus to Bochner-Phillips functional calculus are indicated, and several examples are considered.
arxiv
Noncommutative Chebyshev inequality involving the Hadamard product
, 2018 We present several operator extensions of the Chebyshev inequality for Hilbert space operators. The main version deals with the synchronous Hadamard property for Hilbert space operators.
Bakherad, Mojtaba +1 more
core
Sylvester equations and polynomial separation of spectra [PDF]
arXiv, 2019 Sylvester equations $AX-XB=C$ have unique solutions for all $C$ when the spectra of $A$ and $B$ are disjoint. Here $A$ and $B$ are bounded operators in Banach spaces. We discuss the existence of polynomials $p$ such that the spectra of $p(A)$ and $p(B)$ are well separated, either inside and outside of a circle or separated into different half planes ...
arxiv
Functional Calculus for Semi-Bounded Operators [PDF]
arXiv, 2002 We build on the work by Davies, extending the Helffer-Sj\"ostrand Functional Calculus domain for semi-bounded operators on Banach spaces given a priori controlled growth of the resolvents. We employ Seeley's Extension Theorem to extend smooth functions on the half line to the whole line and thus indirectly define functions of these operators.
arxiv
arXiv, 2003 We prove lower bounds on $||T_t||$, where $T_t$ is a one-parameter semigroup, starting from information on the resolvent norms, i.e. the pseudospectra. We provide a physically important example in which the growth of the semigroup norm cannot be derived from spectral information. The generator is a self-adjoint Schr\"odinger operator, but the semigroup
arxiv
Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula [PDF]
arXiv, 2003 We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators $A_j$ on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii.
arxiv
$H^{\infty}$ functional calculus and square functions on noncommutative $L^p$-spaces [PDF]
arXiv, 2006 In this work we investigate semigroups of operators acting on noncommutative $L^p$-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and $H^\infty$ functional calculus. We discuss several examples of noncommutative diffusion semigroups.
arxiv