Quasielliptic operators and Sobolev type equations. II.
Quasiharmonic fields
Quasiharmonic fields and Beltrami operators
A quasiharmonic field is a pair of vector fields satisfying , , and coupled by a distorsion inequality. For a given , we construct a matrix field such that . This remark in particular shows that the theory of quasiharmonic fields is equivalent (at least locally) to that of elliptic PDEs. Here we stress some properties of our operator and find their applications to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence.
Quasi-invariant subspaces generated by polynomials with nonzero leading terms
We introduce a partial order relation in the Fock space. Applying it we show that for the quasi-invariant subspace [p] generated by a polynomial p with nonzero leading term, a quasi-invariant subspace M is similar to [p] if and only if there exists a polynomial q with the same leading term as p such that M = [q].
Quasi-isometric vector bundles and bounded factorization of holomorphic matrices
We give a sufficient condition for a hermitian holomorphic vector bundle over the disk to be quasi-isometric to the trivial bundle. One consequence is a version of Cartan's lemma on the factorization of matrices with uniform bounds.
Quasi-iteration methods of Chebyshev type for the approximate solution of operator equations
Quasi-linear algebras and integrability (the Heisenberg picture).
Quasilinear elliptic systems in divergence form with weak monotonicity.
Quasilinear hyperbolic equations with hysteresis
Quasilinear hyperbolic equations with hysteresis
Hysteresis operators are illustrated, and a weak formulation is studied for an initial- and boundary-value problem associated to the equation ; here is a (possibly discontinuous) hysteresis operator, is a second order elliptic operator, is a known function. Problems of this sort arise in plasticity, ferromagnetism, ferroelectricity, and so on. In particular an existence result is outlined.
Quasi-multipliers of the algebra of approximable operators and its duals
Let A be the Banach algebra of approximable operators on an arbitrary Banach space X. For the spaces of all bilinear continuous quasi-multipliers of A resp. its dual A* resp. its bidual A**, concrete representations as spaces of operators are given.
Quasi-nilpotent and compact
Quasinilpotent operators in operator Lie algebras II
In this paper, it is proved that the Banach algebra , generated by a Lie algebra ℒ of operators, consists of quasinilpotent operators if ℒ consists of quasinilpotent operators and consists of polynomially compact operators. It is also proved that consists of quasinilpotent operators if ℒ is an essentially nilpotent Engel Lie algebra generated by quasinilpotent operators. Finally, Banach algebras generated by essentially nilpotent Lie algebras are shown to be compactly quasinilpotent.
Quasinormal operators are hyperreflexive
We will prove the statement in the title. We also give a better estimate for the hyperreflexivity constant for an analytic Toeplitz operator.
Quasinormality and numerical ranges of certain classes of dual Toeplitz operators.
Quasi-normed operator ideals on Banach spaces and interpolation.
Quasi-probability distribution of nonclassical states in interacting Fock space
In this paper we study approximate quasi-probability distribution functions of nonclassical states such as incoherent states, Kerr states, squeezed states and k-photon coherent states in interacting Fock space.
Quasireducible operators.
Quasi-retractive representation of solution sets to stochastic inclusions.
Quasireversibility for inhomogeneous ill-posed problems in Hilbert spaces.