Let X be a countable fundamental set in a Hilbert space H, and let T be the operator X x2X c(x)x: Whenever T is well-deened and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is injective is a stable basis (also known as a Riesz basis). This paper considers the above three properties for subspaces H of L 2 ...

We compute the essential norm of a composition operator relatively to the class of Dunford-Pettis opertors or weakly compact operators, on some uniform algebras of analytic functions. Even in the frame of H∞ (resp. the disk algebra), this is new, as well for the polydisk algebras and the polyball algebras. This is a consequence of a general study of weighted composition operators.

In this paper, we show that the property of tight affine frame decomposition of functions in L can be extended in a stable way to functions in Sobolev spaces when the generators of the tight affine frames satisfy certain mild regularity and vanishing moment conditions. Applying the affine frame operators Qj on j-th levels to any function f in a Sobolev space reveals the detailed information Qjf...

This article rst argues that formalisations of the frame prob lem should have certain desirable logical features it then pro poses a treatment of the frame problem using linear logic to gether with modal operators which ful ls these desiderata and seems to be successful in other respects

The purpose of this note is to explain how to use the equivariant method of moving frames, [1, 10], to derive the differential invariants, invariant differential operators and invariant differential forms for surfaces in three-dimensional Euclidean space. This is, of course, a very classical problem and the results are not new; for the classical moving frame derivation, see, for instance, [2, 3...

We discuss concrete examples for frame functions and their associated density operators, as well as for non-Gleason type probability measures.

Mathematical models in the form of differential equations can often not be solved analytically, but need to be simulated by means of a numerical method. Particle methods are mesh-free schemes that use independent or pairwise interacting particles to represent the physical properties of a system. This allows for natural adaptivity in complex or deforming geometries. The Lagrangian frame of refer...

This paper introduces sufficient and necessary conditions with respect to the fuzzy operators considered in a multi-adjoint frame under which the standard combinations of multiadjoint sufficiency, possibility and necessity operators form (antitone or isotone) Galois connections. The underlying idea is to study the minimal algebraic requirements so that the concept-forming operators (defined usi...

In this paper we briefly review a not so well known quadratic, phase invariant image processing operator, the energy operator, and describe its tensor-valued generalization, the energy tensor. We present relations to the real-valued and the complex valued energy operators and discuss properties of the three operators. We then focus on the discrete implementation for estimating the tensor based ...

In this paper, we investigate the existence of extension operators fromW (Ω) toW (R) (1 < p < ∞) for a class of tree-shaped domains Ω with a self-similar fractal boundary previously studied by Mandelbrot and Frame. When the fractal boundary has no self-contact, the results of Jones imply that there exist such extension operators for all p ∈ [1,∞]. In the case when the fractal boundary self-inte...