A Priori Bounds for Semielliptic Operators

A Priori Bounds for a Class of Elliptic Operators

A Priori Bounds for the Riccati Equation

Since the appearance of [6] and [7], the theory of linear filtering has experienced a renaissance. This theory, although evidently well known to statisticians in terms of "least squares estimates," has found many applications in the early sixties, largely because of the realization and synthesis methods provided in [6] and [7]. For an indication ofsome of the aerospace applications to guidance ...

A Priori Bounds for Some Infinitely Renormalizable Quadratics: Ii. Decorations

Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements

We prove optimal bounds for the discretization error of geodesic finite elements for variational partial differential equations for functions that map into a nonlinear space. For this we first generalize the well-known Céa lemma to nonlinear function spaces. In a second step we prove optimal interpolation error estimates for pointwise interpolation by geodesic finite elements of arbitrary order...

A priori estimates for the Hill and Dirac operators

Consider the Hill operator Ty = −y′′ + q′(t)y in L2(R), where q ∈ L2(0, 1) is a 1periodic real potential. The spectrum of T is is absolutely continuous and consists of bands separated by gaps γn, n > 1 with length |γn| > 0. We obtain a priori estimates of the gap lengths, effective masses, action variables for the KDV. For example, if μn are the effective masses associated with the gap γn = (λ ...