In a separable complex Hilbert space endowed with an isometric conjugate-linear involution, we study sequences orthonormal with respect to an associated bilinear form. Properties of such sequences are measured by a positive, possibly unbounded angle operator which is formally orthogonal as a matrix. Although developed in an abstract setting, this framework is relevant to a variety of eigenvecto...

The convergence of new second-order iterative methods are analyzed in Banach spaces by introducing a system of recurrence relations. A system of a priori error bounds for that method is also provided. The methods are defined by using a constant bilinear operator A, instead of the second Fréchet derivative appearing in the defining formula of the Chebyshev method. Numerical evidence that the met...

Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order approximation are not always sufficient and higher order developpements are used in recent works. Motivated by these applications, we give in this paper a criterion that applies to situations where the evolution operator is expressed as sum of possib...

On arbitrary regular quadrilaterals, a new finite element method for the Reissner-Mindlin plate is proposed, where both transverse displacement and rotation are approximated by isoparametric bilinear elements, with local bubbles enriching rotation, and a local reduction operator is applied to the shear energy term. This new method gives optimal error bounds, uniform in the thickness of the plat...

The three bilinearities uv, uv, uv for functions u, v : R2×[0, T ] 7−→ C are sharply estimated in function spaces Xs,b associated to the Schrödinger operator i∂t+∆. These bilinear estimates imply local wellposedness results for Schrödinger equations with quadratic nonlinearity. Improved bounds on the growth of spatial Sobolev norms of finite energy global-in-time and blow-up solutions of the cu...

We formulate a model of relativistic fermions moving in two Euclidean dimensions based on a tight-binding model of graphene. The eigenvalue spectrum of the resulting Dirac operator is solved numerically in smooth U(1) gauge field backgrounds carrying an integer-valued topological charge Q, and it is demonstrated that the resulting number of zero-eigenvalue modes is in accord with the Atiyah-Sin...

To assist the matching of lattice field theory results to high energy continuum limit we evaluate Green's function where tensor quark bilinear operator is inserted at zero momentum in a 2-point for an arbitrary covariant gauge. This carried out both $\overline{\mathrm{MS}}$ and ${\mathrm{RI}}^{\ensuremath{'}}$ schemes four loops. The current anomalous dimension also calculated loops color group.

Approximating the Koopman operator from data is numerically challenging when many lifting functions are considered. Even low-dimensional systems can yield unstable or ill-conditioned results in a high-dimensional lifted space. In this paper, Extended Dynamic Mode Decomposition (DMD) and DMD with control, two methods for approximating operator, reformulated as convex optimization problems linear...

Let b be aBMO-function. It is well-known that the linear commutator [b, T ] of a Calderón-Zygmund operator T does not, in general, map continuously H(R) into L(R). However, Pérez showed that if H(R) is replaced by a suitable atomic subspace H b(R ) then the commutator is continuous from H b(R ) into L(R). In this paper, we find the largest subspace H b (R ) such that all commutators of Calderón...

~ave energy flow conservation is demonstrated for Hermitian differential operators that arise m the Vlasov-Maxwell theory for propagation perpendicular to a magnetic field. The energy fl~w can be related ~o the. bilinear concomitant, for a solution and its complex conjugate, by usmg the Lagrange Identity ofthe operator. This bilinear form obeys a conservation law and is shown to describe the us...